Relevant bibliographies by topics / Fredholm theory

Academic literature on the topic 'Fredholm theory'

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Published: 4 June 2021
Last updated: 29 January 2023

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Journal articles on the topic "Fredholm theory"

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Smyth, M. R. F. "PATHOLOGICAL FREDHOLM THEORY." Mathematical Proceedings of the Royal Irish Academy 113A, no. 2 (2013): 169–83. http://dx.doi.org/10.1353/mpr.2013.0017.

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Smyth, M. R. F. "Pathological Fredholm Theory." Mathematical Proceedings of the Royal Irish Academy 113, no. 2 (January 1, 2013): 169–83. http://dx.doi.org/10.3318/pria.2013.113.15.

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Hofer, Helmut, Kris Wysocki, and Eduard Zehnder. "A general Fredholm theory III: Fredholm functors and polyfolds." Geometry & Topology 13, no. 4 (June 4, 2009): 2279–387. http://dx.doi.org/10.2140/gt.2009.13.2279.

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Perez-Garcia, C., and S. Vega. "Perturbation theory of p-adic Fredholm and semi-Fredholm operators." Indagationes Mathematicae 15, no. 1 (2004): 115–27. http://dx.doi.org/10.1016/s0019-3577(04)90009-2.

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Lindeboom, L., and H. Raubenheimer. "On regularities and Fredholm theory." Czechoslovak Mathematical Journal 52, no. 3 (September 2002): 565–74. http://dx.doi.org/10.1023/a:1021727829750.

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Georgeot, B., and R. E. Prange. "Fredholm Theory for Quasiclassical Scattering." Physical Review Letters 74, no. 21 (May 22, 1995): 4110–13. http://dx.doi.org/10.1103/physrevlett.74.4110.

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Eschmeier, Jörg. "Samuel multiplicity and Fredholm theory." Mathematische Annalen 339, no. 1 (May 3, 2007): 21–35. http://dx.doi.org/10.1007/s00208-007-0103-5.

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BENJAMIN, RONALDA, NIELS JAKOB LAUSTSEN, and SONJA MOUTON. "r-FREDHOLM THEORY IN BANACH ALGEBRAS." Glasgow Mathematical Journal 61, no. 03 (September 25, 2018): 615–27. http://dx.doi.org/10.1017/s0017089518000393.

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AbstractHarte (1982, Math. Z. 179, 431–436) initiated the study of Fredholm theory relative to a unital homomorphism T: A → B between unital Banach algebras A and B based on the following notions: an element a ∈ A is called Fredholm if 0 is not in the spectrum of Ta, while a is Weyl (Browder) if there exist (commuting) elements b and c in A with a = b + c such that 0 is not in the spectrum of b and c is in the null space of T. We introduce and investigate the concepts of r-Fredholm, r-Weyl and r-Browder elements, where 0 in these definitions is replaced by the spectral radii of a and b, respectively.
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Carpintero, C., A. Gutierrez, E. Rosas, and J. Sanabria. "A note on preservation of generalized Fredholm spectra in Berkani’s sense." Filomat 32, no. 18 (2018): 6431–40. http://dx.doi.org/10.2298/fil1818431c.

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In this paper, we study the relationships between the spectra derived from B-Fredholm theory corresponding to two given bounded linear operators. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from B-Fredholm theory corresponding to two given operators are respectively the same. Among other results, we prove that B-Fredholm type spectral properties for an operator and its restriction are equivalent, as well as obtain conditions for which B-Fredholm type spectral properties corresponding to two given operators are the same. As application of our results, we obtain conditions for which the above mentioned spectra and the spectra derived from the classical Fredholm theory are the same.
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Ammar, Aymen, Slim Fakhfakh, and Aref Jeribi. "Fredholm theory for demicompact linear relations." Applied General Topology 23, no. 2 (October 3, 2022): 425–36. http://dx.doi.org/10.4995/agt.2022.16940.

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We first attempt to determine conditions on a linear relation T such that μT becomes a demicompact linear relation for each μ ∈ [0,1)(see Theorems 2.4 and 2.5). Second, we display some results on Fredholm and upper semi-Fredholm linear relations involving a demicompact one(see Theorems 3.1 and 3.2). Finally, we provide some results in which a block matrix of linear relations becomes a demicompact block matrix of linear relations (see Theorems 4.2 and 4.3).
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Dissertations / Theses on the topic "Fredholm theory"

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Heymann, Retha. "Fredholm theory in general Banach algebras." Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/4265.

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Thesis (MSc (Mathematics))--University of Stellenbosch, 2010.
ENGLISH ABSTRACT: This thesis is a study of a generalisation, due to R. Harte (see [9]), of Fredholm theory in the context of bounded linear operators on Banach spaces to a theory in a Banach algebra setting. A bounded linear operator T on a Banach space X is Fredholm if it has closed range and the dimension of its kernel as well as the dimension of the quotient space X/T(X) are finite. The index of a Fredholm operator is the integer dim T−1(0)−dimX/T(X). Weyl operators are those Fredholm operators of which the index is zero. Browder operators are Fredholm operators with finite ascent and descent. Harte’s generalisation is motivated by Atkinson’s theorem, according to which a bounded linear operator on a Banach space is Fredholm if and only if its coset is invertible in the Banach algebra L(X) /K(X), where L(X) is the Banach algebra of bounded linear operators on X and K(X) the two-sided ideal of compact linear operators in L(X). By Harte’s definition, an element a of a Banach algebra A is Fredholm relative to a Banach algebra homomorphism T : A ! B if Ta is invertible in B. Furthermore, an element of the form a + b where a is invertible in A and b is in the kernel of T is called Weyl relative to T and if ab = ba as well, the element is called Browder. Harte consequently introduced spectra corresponding to the sets of Fredholm, Weyl and Browder elements, respectively. He obtained several interesting inclusion results of these sets and their spectra as well as some spectral mapping and inclusion results. We also convey a related result due to Harte which was obtained by using the exponential spectrum. We show what H. du T. Mouton and H. Raubenheimer found when they considered two homomorphisms. They also introduced Ruston and almost Ruston elements which led to an interesting result related to work by B. Aupetit. Finally, we introduce the notions of upper and lower semi-regularities – concepts due to V. M¨uller. M¨uller obtained spectral inclusion results for spectra corresponding to upper and lower semi-regularities. We could use them to recover certain spectral mapping and inclusion results obtained earlier in the thesis, and some could even be improved.
AFRIKAANSE OPSOMMING: Hierdie tesis is ‘n studie van ’n veralgemening deur R. Harte (sien [9]) van Fredholm-teorie in die konteks van begrensde lineˆere operatore op Banachruimtes tot ’n teorie in die konteks van Banach-algebras. ’n Begrensde lineˆere operator T op ’n Banach-ruimte X is Fredholm as sy waardeversameling geslote is en die dimensie van sy kern, sowel as di´e van die kwosi¨entruimte X/T(X), eindig is. Die indeks van ’n Fredholm-operator is die heelgetal dim T−1(0) − dimX/T(X). Weyl-operatore is daardie Fredholm-operatore waarvan die indeks gelyk is aan nul. Fredholm-operatore met eindige styging en daling word Browder-operatore genoem. Harte se veralgemening is gemotiveer deur Atkinson se stelling, waarvolgens ’n begrensde lineˆere operator op ’n Banach-ruimte Fredholm is as en slegs as sy neweklas inverteerbaar is in die Banach-algebra L(X) /K(X), waar L(X) die Banach-algebra van begrensde lineˆere operatore op X is en K(X) die twee-sydige ideaal van kompakte lineˆere operatore in L(X) is. Volgens Harte se definisie is ’n element a van ’n Banach-algebra A Fredholm relatief tot ’n Banach-algebrahomomorfisme T : A ! B as Ta inverteerbaar is in B. Verder word ’n Weyl-element relatief tot ’n Banach-algebrahomomorfisme T : A ! B gedefinieer as ’n element met die vorm a + b, waar a inverteerbaar in A is en b in die kern van T is. As ab = ba met a en b soos in die definisie van ’n Weyl-element, dan word die element Browder relatief tot T genoem. Harte het vervolgens spektra gedefinieer in ooreenstemming met die versamelings van Fredholm-, Weylen Browder-elemente, onderskeidelik. Hy het heelparty interessante resultate met betrekking tot insluitings van die verskillende versamelings en hulle spektra verkry, asook ’n paar spektrale-afbeeldingsresultate en spektraleinsluitingsresultate. Ons dra ook ’n verwante resultaat te danke aan Harte oor, wat verkry is deur van die eksponensi¨ele-spektrum gebruik te maak. Ons wys wat H. du T. Mouton en H. Raubenheimer verkry het deur twee homomorfismes gelyktydig te beskou. Hulle het ook Ruston- en byna Rustonelemente gedefinieer, wat tot ’n interessante resultaat, verwant aan werk van B. Aupetit, gelei het. Ten slotte stel ons nog twee begrippe bekend, naamlik ’n onder-semi-regulariteit en ’n bo-semi-regulariteit – konsepte te danke aan V. M¨uller. M¨uller het spektrale-insluitingsresultate verkry vir spektra wat ooreenstem met bo- en onder-semi-regulariteite. Ons kon dit gebruik om sekere spektrale-afbeeldingsresultate en spektrale-insluitingsresultate wat vroe¨er in hierdie tesis verkry is, te herwin, en sommige kon selfs verbeter word.
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Bogveradze, Giorgi. "Fredholm theory for Wiener-Hopf plus Hankel operators." Doctoral thesis, Universidade de Aveiro, 2008. http://hdl.handle.net/10773/2935.

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Doutoramento em Matemática
Na presente tese consideramos combinações algébricas de operadores de Wiener-Hopf e de Hankel com diferentes classes de símbolos de Fourier. Nomeadamente, foram considerados símbolos matriciais na classe de elementos quase periódicos, semi-quase periódicos, quase periódicos por troços e certas funções matriciais sectoriais. Adicionalmente, foi dedicada atenção também aos operadores de Toeplitz mais Hankel com símbolos quase periódicos por troços e com símbolos escalares possuindo n pontos de discontinuidades quase periódicas usuais. Em toda a tese, um objectivo principal teve a ver com a obtenção de descrições para propriedades de Fredholm para estas classes de operadores. De forma a deduzir a invertibilidade lateral ou bi-lateral para operadores de Wiener-Hopf mais Hankel com símbolos matriciais AP foi introduzida a noção de factorização assimétrica AP. Neste âmbito, foram dadas condições suficientes para a invertibilidade lateral e bi-lateral de operadores de Wiener- Hopf mais Hankel com símbolos matriciais AP. Para tais operadores, foram ainda exibidos inversos generalizados para todos os casos possíveis. Para os operadores de Wiener-Hopf-Hankel com símbolos matriciais SAP e PAP foi deduzida a propriedade de Fredholm e uma fórmula para a soma dos índices de Fredholm destes operadores de Wiener-Hopf mais Hankel e operadores de Wiener-Hopf menos Hankel. Uma versão mais forte destes resultados foi obtida usando a factorização generalizada AP à direita. Foram analisados os operadores de Wiener-Hopf-Hankel com símbolos que apresentam determinadas propriedades pares e também com símbolos de Fourier que contêm matrizes sectoriais. Em adição, para operadores de Wiener-Hopf-Hankel, foi obtido um resultado correspondente ao teorema clássico de Douglas e Sarason conhecido para operadores de Toeplitz com símbolos sectoriais e unitários. Condições necessárias e suficientes foram também deduzidas para que os operadores de Wiener-Hopf mais Hankel com símbolos L∞ sejam de Fredholm (ou invertíveis). Para se obter tal resultado, trabalhou-se com certas factorizações ímpares dos símbolos de Fourier. Os operadores de Toeplitz mais Hankel gerados por símbolos que possuem n pontos de discontinuidades quase periódicas usuais foram também considerados. Foram obtidas condições sob as quais estes operadores são invertíveis à direita e com dimensão de núcleo infinita, invertíveis à esquerda e com dimensão de co-núcleo infinita ou não normalmente solúveis. A nossa atenção foi também colocada em operadores de Toeplitz mais Hankel com símbolos matriciais contínuos por troços. Para tais operadores, condições necessárias e suficientes foram obtidas para se ter a propriedade de Fredholm. Tal foi realizado usando a abordagem do cálculo simbólico, determinados operadores auxiliares emparelhados com símbolos semi-quase periódicos e várias relações de equivalência após extensão entre operadores.
In this thesis we considered algebraic combinations of Wiener-Hopf and Hankel operators with different classes of Fourier symbols. Namely, matrix symbols from the almost periodic, semi-almost periodic, piecewise almost periodic and certain sectorial matrix functions were considered. In addition, attention was also paid to Toeplitz plus Hankel operators with piecewise almost periodic symbols and with scalar symbols having n points of standard almost periodic discontinuities. In the entire thesis a main goal is to obtain Fredholm properties description of those classes of operators. To deduce the lateral or both sided invertibility theory for Wiener-Hopf plus Hankel operators with AP matrix symbols was introduced the notion of an AP asymmetric factorization. In this framework were given sufficient conditions for the lateral and both sided invertibility of the Wiener-Hopf plus Hankel operators with matrix AP symbols. For such kind of operators were also exhibited generalized inverses for all the possible cases. For the Wiener-Hopf-Hankel operators with matrix SAP and PAP symbols the Fredholm property and a formula for the sum of the Fredholm indices of these Wiener-Hopf plus Hankel and Wiener-Hopf minus Hankel operators were derived. A stronger version of these results was obtained by using the generalized right AP factorization. It was analyzed the Wiener-Hopf-Hankel operators with symbols presenting some even properties, and also with Fourier symbols which contain sectorial matrices. In addition, for Wiener-Hopf-Hankel operators, it was obtained a corresponding result to the classical theorem by Douglas and Sarason known for Toeplitz operators with sectorial and unitary valued symbols. Necessary and sufficient condition for the Wiener-Hopf plus Hankel operators with L∞ symbols to be Fredholm (or invertible) were also derived. To obtain such a result we dealt with certain odd asymmetric factorization of the Fourier symbols. The Toeplitz plus Hankel operators generated by symbols which have n points of standard almost periodic discontinuities were also considered. Conditions were obtained under which these operators are right-invertible and with infinite kernel dimension, left-invertible and with infinite cokernel dimension or simply not normally solvable. We also focused our attention to Toeplitz plus Hankel operators with piecewise almost periodic matrix symbols. For such operators necessary and sufficient conditions were obtained to have the Fredholm property. This was done using a symbol calculus approach, certain auxiliary paired operators with semi-almost periodic symbols, and several equivalence after extension operator relations.
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Covarrubias, Enrique. "General equilibrium theory in infinite dimensions : an application of Fredholm Index Theory." Thesis, University of Edinburgh, 2009. http://hdl.handle.net/1842/12016.

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This thesis deals with generic determinacy and the number of equilibria for infinite dimensional economies. Our work could be seen as an infinite-dimensional analogue of Dierker and Dierker (1972) by characterising equilibria of an economy as a zero of the aggregate excess demand and studying its transversality. In this case, we can use extensions of the Sard-Smale theorem. Assuming separable utilities we give a new proof of generic determinacy of equilibria. We define regular price systems in this setting and show that an economy is regular if and only if its associated excess demand function only has regular equilibrium prices. We also define the infinite equilibrium manifold à la Balasko and show that it has the structure of a Banach manifold. We provide conditions that guarantee global uniqueness of equilibria for smooth infinite economies. We do this by introducing to the economic literature the notion of Z-Rothe vector fields that will allow us to construct an index theorem à la Dierker (1972); this shows that the number of equilibria is odd and in particular gives a new proof of existence. Extending the finite dimensional results of Balasko (1988), we characterise the equilibrium manifold as a covering space of the set of economies and we study global conditions under which the natural projection map is a diffeomorphism. We finally study the effects that critical equilibria have on the global invertibility of the natural projection map.
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Lindner, Marko. "Fredholm Theory and Stable Approximation of Band Operators and Their Generalisations." Doctoral thesis, Universitätsbibliothek Chemnitz, 2009. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200901182.

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This text is concerned with the Fredholm theory and stable approximation of bounded linear operators generated by a class of infinite matrices $(a_{ij})$ that are either banded or have certain decay properties as one goes away from the main diagonal. The operators are studied on $\ell^p$ spaces of functions $\Z^N\to X$, where $p\in[1,\infty]$, $N\in\N$ and $X$ is a complex Banach space. The latter means that our matrix entries $a_{ij}$ are indexed by multiindices $i,j\in\Z^N$ and that every $a_{ij}$ is itself a bounded linear operator on $X$. Our main focus lies on the case $p=\infty$, where new results are derived, and it is demonstrated in both general theory and concrete operator equations from mathematical physics how advantage can be taken of these new $p=\infty$ results in the general case $p\in[1,\infty]$.
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Hagger, Raffael [Verfasser], and Marko [Akademischer Betreuer] Lindner. "Fredholm Theory with Applications to Random Operators / Raffael Hagger. Betreuer: Marko Lindner." Hamburg : Universitätsbibliothek der Technischen Universität Hamburg-Harburg, 2016. http://d-nb.info/1081423633/34.

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Côme, Rémi. "Analyse sur les espaces singuliers et théorie de l’indice." Electronic Thesis or Diss., Université de Lorraine, 2020. http://www.theses.fr/2020LORR0096.

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Le contexte général de cette thèse est celui de l'extension de la théorie des opérateurs elliptiques, bien connue dans le cadre lisse, à des domaines dits singuliers. Les méthodes utilisées reposent d'une part sur l'emploi d'algèbres d'opérateurs et d'outils issus de la géométrie non commutative, d'autre part sur l'introduction de calculs pseudodifférentiels adaptés à la géométrie du domaine, souvent via un groupoïde qui résout les singularités. La première partie de la thèse s'intéresse à l'étude d'une classe particulière de ces groupoïdes, dits Fredholm, qui donnent un cadre très favorable à l'analyse des opérateurs elliptiques. Un des résultats majeurs obtenu est que cette propriété de Fredholm est locale, au sens où elle ne dépend que des restrictions du groupoïde à un nombre suffisant d'ouverts. Dans le même esprit, nous considérons avec C. Carvalho et Y. Qiao des groupoïdes obtenus comme recollements d'actions de groupes, et étudions en particulier un groupoïde adapté à l'étude des opérateurs potentiels de couche. Je conclus cette partie avec la résolution d'un problème aux limites pour un domaine à singularité de type cusp rotationnel. La seconde partie s'intéresse aux opérateurs équivariants sur des variétés compactes, sous l'action d'un groupe fini. On répond à la question suivante : étant donnée une représentation irréductible du groupe, à quelle condition un opérateur différentiel est-il Fredholm entre les composantes isotypiques correspondantes des espaces de Sobolev ? Dans un travail commun avec A. Baldare, M. Lesch et V. Nistor, nous définissons une notion correspondante d'ellipticité associée à une représentation irréductible fixée et montrons qu'elle caractérise les opérateurs de Fredholm
This thesis is set in the general context of extending the theory of elliptic operators, well-understood in the smooth setting, to so-called singular domains. The methods used rely on operator algebras and tools coming from non commutative geometry, together with suitable pseudodifferential calculi that are often built from a groupoid adapted to the particular geometry of the problem. The first part of the thesis deals with the general investigation of a particular class of such groupoids, called Fredholm, that provide a very good setting for the study of elliptic operators. One of the major results proved here is that this Fredholm property is local, in the sense that it only depends on the restrictions of the groupoid to sufficiently many open subsets. In the same spirit, we study with C. Carvalho and Y. Qiao groupoids whose local structure is given by gluing group actions, and consider in particular a groupoid suited to the study of layer potential operators. This part concludes with a well-posedness result for a boundary value problem on a domain with a rotational cusp. The second part deals with equivariant operators on a compact manifold, acted upon by a finite group. We answer the following question: given an irreducible representation of the group, under which condition is a differential operator Fredholm between the corresponding isotypical components of the Sobolev spaces? In a joint work with A. Baldare, M. Lesch and V. Nistor, we introduce a corresponding notion of ellipticity associated with some fixed irreducible representation, and show that it characterizes Fredholm operators
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Veloso, Diogo. "Seiberg-Witten theory on 4-manifolds with periodic ends." Thesis, Aix-Marseille, 2014. http://www.theses.fr/2014AIXM4781/document.

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Dans cette thèse on prouve des résultats analytiques sur la théorie cohomotopique de Seiberg-Witten pour des 4-variétes Riemanniennes Spinc(4) a bouts périodiques, (X,g,τ). Nos résultats montrent, que sur certaines conditions techniques en (X, g, τ ),, cette nouvelle version est cohérente et mène a des invariants de Seiberg-Witten.Premièrement, en utilisant le critère de Taubes pour des operateurs périodiques dans des variétes a bouts périodiques, on montre que pour une 4-varieté Riemmanienne a bouts périodiques (X, g) vérifiant certaines conditions topologiques, le Laplacian ∆+ : L2(Λ2+) → L2(Λ2+) est un opérateur de Fredholm. On prouve une décomposition de type Hodge pour des 1-formes de X, a poids positif.Ensuite on prouve, en assumant certaines conditions topologiques et courbure scalaire non-negative sur les bouts, que l'opérateur de Dirac associé a une connection périodique (ASD a l'infini) est Fredholm.Dans la deuxième partie de la thèse on démontre un isomorphisme entre le groupe de cohomologie de de Rham Hd1R(X,iR), et le groupe harmonique intervenant dans la decomposition de Hodge des 1-formes de X a poids positif. On prouve l'existence de deux séquences exactes courtes liant le groupe de jauge de l'espace de modules de Seiberg-Witten et le groupe de cohomologie H1(X, 2πiZ).Dans la troisième partie on prouve les principaux résultats: la coercitivité de l'application de Seiberg-Witten et la compacité de l'espace de moduli pour une 4-varieté a bouts périodiques (X, g, τ ), vérifiant les conditions mentionnées plus haut.Finalment, utilisant la coercivité, on montre l'existence d'un invariant cohomotopique de type Seiberg- Witten type associé a (X, g, τ )
In this thesis we prove analytic results about a cohomotopical Seiberg-Witten theory for a Riemannian, Spinc(4) 4-manifold with periodic ends, (X,g,τ) . Our results show that, under certain technical assumptions on (X, g, τ ), this new version is coher- ent and leads to Seiberg-Witten type invariants for this new class of 4-manifolds.First, using Taubes criteria for end-periodic operators on manifolds with periodic ends, we show that, for a Riemannian 4-manifold with periodic ends (X, g), verifying certain topological conditions, the Laplacian ∆+ : L2(Λ2+) → L2(Λ2+) is a Fredholm operator. This allows us to prove an important Hodge type decomposition for positively weighted Sobolev 1-forms on X.We prove, assuming non-negative scalar curvature on each end and certain technical topological conditions, that the associated Dirac operator associated with an end-periodic connection (which is ASD at infinity) is Fredholm.In the second part of the thesis we establish an isomorphism between be- tween the de Rham cohomology group, Hd1R(X,iR) (which is a topological in- variant of X) and the harmonic group intervening in the above Hodge type decomposition of the space of positively weighted 1-forms on X. We also prove two short exact sequences relating the gauge group of our Seiberg-Witten moduli problem and the cohomology group H1(X, 2πiZ).In the third part, we prove our main results: the coercivity of the Seiberg-Witten map and compactness of the moduli space for a 4-manifold with periodic ends (X,g,τ) verifying the above conditions.Finally, using our coercitivity property, we show that a Seiberg-Witten type cohomotopy invariant associated to (X, g, τ ) can be defined
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Seidel, Markus. "On some Banach Algebra Tools in Operator Theory." Doctoral thesis, Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-83750.

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Die vorliegende Arbeit ist der Untersuchung von Operatorfolgen gewidmet, die typischerweise bei der Anwendung von Approximationsverfahren auf stetige lineare Operatoren entstehen. Dabei stehen die Stabilität der Folgen sowie das asymptotische Verhalten gewisser Charakteristika wie Normen, Konditionszahlen, Fredholmeigenschaften und Pseudospektren im Mittelpunkt. Das Hauptaugenmerk liegt auf der Entwicklung der Theorie für Operatoren auf Banachräumen. Hierbei bildet ein dafür geeigneter Konvergenzbegriff, die sogenannte P-starke Konvergenz, den Ausgangspunkt, welcher das Studium der gewünschten Eigenschaften in einer erstaunlichen Allgemeinheit gestattet. Die erzielten Resultate kommen, neben einer Reihe weiterer Anwendungen, insbesondere für das Projektionsverfahren für banddominierte Operatoren zum Einsatz.
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Ehrhardt, Torsten. "Factorization theory for Toeplitz plus Hankel operators and singular integral operators with flip." Doctoral thesis, [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=972573305.

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Acevedo, Jeovanny de Jesus Muentes. "O fluxo espectral de caminhos de operadores de Fredholm auto-adjuntos em espaços de Hilbert." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-01122017-214259/.

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O objetivo principal desta dissertação é apresentar o fluxo espectral de um caminho de operadores de Fredholm auto-adjuntos em um espaço de Hilbert e suas propriedades. Pelos resultados clássicos de teoria espectral, sabemos que se H é um espaço de Hilbert e L : H → H é um operador linear, limitado e auto-adjunto, H pode ser escrito como soma direta ortogonal H+(L)⊕ H-(L)⊕ Ker L, onde H+(L) e H-(L) são os subespaços espectrais positivo e negativo de L, respectivamente. No trabalho damos uma definição de fluxo espectral baseada na decomposição acima, aprofundando as conexões deste conceito com a teoria espectral dos operadores de Fredholm em espaços de Hilbert. Entre as propriedades do fluxo espectral, será analisada a invariância homotópica que se apresenta em várias formas. Veremos o conceito de índice de Morse relativo, que estende o clássico índice de Morse, e sua relação com o fluxo espectral. A construção do fluxo espectral dada neste trabalho segue a abordagem de P. M. Fitzpatrick, J. Pejsachowicz e L. Recht em [9].
The main purpose of this dissertation is to present the spectral flow of a path of selfadjoint Fredholm operators in a Hilbert space and its properties. By classical results in spectral theory, we know that, if H is a Hilbert space and L : H → H is a bounded self-adjoint linear operator, H may be written as the following orthogonal direct sum H = H+(L)⊕ H-(L)⊕ Ker L, where H+(L) and H-(L) are the positive and negative spectral subspaces of L, respectively. In this work we give a definition of spectral flow which is based on the above splitting, examining in depth the connection between this concept and the spectral theory of Fredholm operators in Hilbert spaces. Among the properties of the spectral flow we will analyze the homotopic invariance, which appears on different ways. We will see the concept of relative Morse index, which generalize the classical Morse index, and its relation with the spectral flow. The construction of the spectral flow given in this work follows the approach of P. M. Fitzpatrick, J. Pejsachowicz and L. Recht in [9].
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Books on the topic "Fredholm theory"

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Fredholm theory in Banach spaces =: Theori Fredholm yng ngofodau Banach. Cambridge: Cambridge University Press, 1986.

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Hofer, Helmut, Krzysztof Wysocki, and Eduard Zehnder. Polyfold and Fredholm Theory. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-78007-4.

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Aiena, Pietro. Fredholm and Local Spectral Theory II. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-02266-2.

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Carey, Alan, and Galina Levitina. Index Theory Beyond the Fredholm Case. Cham: Springer Nature Switzerland, 2022. http://dx.doi.org/10.1007/978-3-031-19436-8.

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Operator theory and arithmetic in H [infinity]. Providence, R.I: American Mathematical Society, 1988.

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I͡Anushauskas, Alʹgimantas Ionosovich. The oblique derivative problem of potential theory. New York: Consultants Bureau, 1989.

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service), SpringerLink (Online, ed. Elliptic Partial Differential Equations: Volume 1: Fredholm Theory of Elliptic Problems in Unbounded Domains. Basel: Springer Basel AG, 2011.

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Ziltener, Fabian. A quantum Kirwan map: Bubbling and Fredholm theory for symplectic vortices over the plane. Providence, Rhode Island: American Mathematical Society, 2014.

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1941-, Booss Bernhelm, Grubb Gerd, and Wojciechowski Krzysztof P. 1953-, eds. Spectral geometry of manifolds with boundary and decomposition of manifolds: Proceedings of the Workshop on Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds, Roskilde University, Roskilde, Denmark, August 6-9, 2003. Providence, R.I: American Mathematical Society, 2005.

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1973-, Lindner Marko, ed. Limit operators, collective compactness, and the spectral theory of infinite matrices. Providence, R.I: American Mathematical Society, 2010.

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Book chapters on the topic "Fredholm theory"

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Pipkin, Allen C. "Fredholm Theory." In Texts in Applied Mathematics, 1–27. New York, NY: Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4612-4446-2_1.

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Conway, John B. "Fredholm Theory." In A Course in Functional Analysis, 353–74. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4757-3828-5_11.

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Aiena, Pietro. "Fredholm Theory." In Fredholm and Local Spectral Theory II, 1–94. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-02266-2_1.

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Kubrusly, Carlos S. "Fredholm Theory." In Spectral Theory of Operators on Hilbert Spaces, 131–86. Boston: Birkhäuser Boston, 2012. http://dx.doi.org/10.1007/978-0-8176-8328-3_5.

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Conway, John B. "Fredholm Theory." In A Course in Functional Analysis, 347–68. New York, NY: Springer New York, 2007. http://dx.doi.org/10.1007/978-1-4757-4383-8_11.

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Simon, Barry. "Fredholm theory." In Mathematical Surveys and Monographs, 45–52. Providence, Rhode Island: American Mathematical Society, 2010. http://dx.doi.org/10.1090/surv/120/05.

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Cheverry, Christophe, and Nicolas Raymond. "FREDHOLM THEORY." In A Guide to Spectral Theory, 101–21. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-67462-5_5.

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Ryzhov, Vladimir, Tatiana Fedorova, Kirill Safronov, Shaharin Anwar Sulaiman, and Samsul Ariffin Abdul Karim. "Fredholm Theory." In Modern Methods in Mathematical Physics, 69–123. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-4915-9_3.

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Bercovici, Hari. "Fredholm theory." In Mathematical Surveys and Monographs, 181–230. Providence, Rhode Island: American Mathematical Society, 1988. http://dx.doi.org/10.1090/surv/026/07.

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Malkowsky, Eberhard, and Vladimir Rakočević. "Fredholm Theory." In Advanced Functional Analysis, 285–332. Boca Raton, Florida : CRC Press, [2019]: CRC Press, 2019. http://dx.doi.org/10.1201/9780429442599-8.

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Conference papers on the topic "Fredholm theory"

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JOACHIM, MICHAEL. "UNBOUNDED FREDHOLM OPERATORS AND K-THEORY." In Proceedings of the School. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704443_0009.

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Cramer, David, and Yuri Latushkin. "Fredholm determinants and the Evans function for difference equations." In Perspectives in Operator Theory. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc75-0-7.

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Samokhin, A. B., and A. S. Samokhina. "Fredholm integral equations: Scattering on dielectric structures." In 2016 URSI International Symposium on Electromagnetic Theory (EMTS). IEEE, 2016. http://dx.doi.org/10.1109/ursi-emts.2016.7571439.

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Daniele, Vito G., Guido Lombardi, and Rodolfo S. Zich. "The Fredholm Factorization in Presence of Penetrable Rectangular Rods." In 2019 URSI International Symposium on Electromagnetic Theory (EMTS). IEEE, 2019. http://dx.doi.org/10.23919/ursi-emts.2019.8931521.

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Hafftka, Ariel, Hasan Celik, Alexander Cloninger, Wojciech Czaja, and Richard G. Spencer. "2D sparse sampling algorithm for ND Fredholm equations with applications to NMR relaxometry." In 2015 International Conference on Sampling Theory and Applications (SampTA). IEEE, 2015. http://dx.doi.org/10.1109/sampta.2015.7148914.

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LÓPEZ-GÓMEZ, JULIÁN, and CARLOS MORA-CORRAL. "LOCAL SMITH FORM AND EQUIVALENCE FOR ONE-PARAMETER FAMILIES OF FREDHOLM OPERATORS OF INDEX ZERO." In Spectral Theory and Nonlinear Analysis with Applications to Spatial Ecology. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701589_0007.

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Biletskyy, Vasyl, and Sergiy Yaroshko. "A Method of Generalized Separation of Variables for Solving Many-Dimensional Linear Fredholm Integral Equations." In 2007 XIIth International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory. IEEE, 2007. http://dx.doi.org/10.1109/diped.2007.4373583.

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Varnhorn, W. "Maximum Modulus Estimates for the Linear Steady Stokes Equations in Domains of Rn(n ? 2)." In Topical Problems of Fluid Mechanics 2022. Institute of Thermomechanics of the Czech Academy of Sciences, 2022. http://dx.doi.org/10.14311/tpfm.2022.025.

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A maximum modulus estimate for the Stokes system in bounded and unbounded domains of Rn(n 2) is established via methods of hydrodynamical potential theory. Using a suitable potential ansatz in form of hydrodynamical layer potentials the method is based on the unique solvability of the resulting boundary integral equations' system of Fredholm type. In addition, in case of bounded domains, a projection onto the normal eld on the boundary is required.
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Martinez, Rudolph, Brent S. Paul, Morgan Eash, and Carina Ting. "A Three-Dimensional Wiener-Hopf Technique for General Bodies of Revolution: Part 1—Theory." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-13344.

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This work, the first of two parts, presents the development of a new analytic solution of acoustic scattering and/or radiation by arbitrary bodies of revolution under heavy fluid loading. The approach followed is the construction of a three-dimensional Wiener-Hopf technique with Fourier transforms that operate on the finite object’s arclength variable (the object’s practical finiteness comes about, in a Wiener-Hopf sense, by formally bringing to zero the radius of its semi-infinite generator curve for points beyond a prescribed station). Unlike in the classical case of a planar semi-infinite geometry, the kernel of the integral equation is non-translational and therefore with independent wavenumber spectra for its receiver and source arclengths. The solution procedure begins by applying a symmetrizing spatial operator that reconciles the regions of (+) and (−) analyticity of the kernel’s two-wavenumber transform with those of the virtual sources. The spatially symmetrized integral equation is of the Fredholm 2nd kind and thus with a strong unit “diagonal” — a feature that makes possible the Wiener-Hopf factorization of its transcendental doubly-transformed kernel via secondary spectral manipulations. The companion paper [1] will present a numerical demonstration of the new analysis for canonical problems of fluid-structure interaction for finite bodies of revolution.
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Lu, Jian-Fei, Bin Xu, and Jian-Hua Wang. "Vibration Isolation Using Pile Rows in a Layered Poroelastic Half-Space Against the Vibration Due to Harmonic Loads." In ASME 2010 29th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/omae2010-21171.

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The isolation of the vibration due to a harmonic vertical load using pile rows embedded in a layered poroelastic half-space is investigated in this study. Based on Biot’s theory, the frequency domain fundamental solution for a vertical circular patch load applied in a layered poroelastic half-space is derived via the transmission and reflection matrices (TRM) method. Utilizing Muki and Sternberg’s method, the second kind of Fredholm integral equations describing the dynamic interaction between the pile rows and the layered poroelastic half-space subjected to a harmonic vertical load is constructed. The isolation effect of piles rows for the vibration due to the harmonic vertical load is investigated via numerical solution of the integral equations. Numerical results of this study show that a stiffer upper layer overlying a softer bottom half-space will worsen the vibration isolation effect of pile rows and vice versa. Also, pile rows with large length are preferable for a better vibration isolation effect.
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