Dissertations / Theses on the topic 'Toeplitz operator'
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Fedchenko, Dmitry, and Nikolai Tarkhanov. "A Class of Toeplitz Operators in Several Variables." Universität Potsdam, 2013. http://opus.kobv.de/ubp/volltexte/2013/6893/.
Full textBrowning, Brian L. "Time and frequency domain scattering for the one-dimensional wave equation /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/5788.
Full textSeidel, Markus Silbermann Bernd. "Über die Splitting-Eigenschaft der Approximationszahlen von Matrix-Folgen : l1-Theorie$nElektronische Ressource /." [S.l. : s.n.], 2006.
Find full textVasilyev, Vladimir. "Invertibility of a Class of Toeplitz Operators over the Half Plane." Doctoral thesis, Universitätsbibliothek Chemnitz, 2007. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200700157.
Full textVasil'ev, Vladimir A. Silbermann Bernd. "Second-order trace formulas in Szegö-type theorems." [S.l. : s.n.], 2007.
Find full textVasil'ev, Vladimir A. "Invertibility of a class of Toeplitz operators over the half plane." [S.l. : s.n.], 2007.
Find full textEhrhardt, 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.
Full textArroussi, Hicham. "Function and Operator Theory on Large Bergman spaces." Doctoral thesis, Universitat de Barcelona, 2016. http://hdl.handle.net/10803/395175.
Full textBöttcher, A., and S. M. Grudsky. "Estimates for the condition numbers of large semi-definite Toeplitz matrices." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801238.
Full textBarusseau, Benoit. "Propriétés spectrales des opérateurs de Toeplitz." Thesis, Bordeaux 1, 2010. http://www.theses.fr/2010BOR14027/document.
Full textThis thesis deals with the spectral properties of the Toeplitz operators in relation to their associated symbol. In the first part, we give some classical results about Hardy space, model spaces and Bergman space. Afterwards, we expose some results about Toeplitz operator on the Hardy space. In particular, we discuss their spectrum and essential spectrum. Our work is inspired from two facts which have been proved on the Hardy space. First, considering a Toeplitz operator T, the norm, essential norm, spectral radius of T and the supremum of its symbol are equal. Secondly, on the Hardy space, spectrum, essential spectrum and essential range are strongly related. We answer the question of the equality between the norms, the spectral radius and the supremum of the symbol and between spectrum and essential range on the Bergman space. We look at these two properties on the Bergman space when the symbol is radial or quasihomogeneous. We answer these questions using the Berezin transform, the Mellin coefficients and the mean value of the symbol. The last part deals with the classical Szegö theorem which underline a link between the eigenvalues of a Toeplitz matrix sequence and its symbol. We give a result of the same type on Bergman space considering harmonic symbol wich have a continuous extension. We give a generalization, considering the sequence of the compressions of a Toeplitz operator on a sequence of model spaces
Rouby, Ophélie. "Conditions de quantification de Bohr-Sommerfeld pour des opérateurs semi-classiques non auto-adjoints." Thesis, Rennes 1, 2016. http://www.theses.fr/2016REN1S051/document.
Full textWe interest ourselves in the spectral theory of non self-adjoint semi-classical operators in dimension one and in asymptotic expansions of eigenvalues. These expansions are written in terms of geometrical objects in a complex phase space coming from classical mechanics and correspond to a generalization of Bohr-Sommerfeld quantization conditions in the non self-adjoint case. First, we study non self-adjoint perturbations of self-adjoint pseudo-differential operators in dimension one by using techniques of analytic microlocal analysis. As a corollary, we establish for PT-symmetric perturbations of self-adjoint operators, that the spectrum is real. Then we show Bohr-Sommerfeld quantization conditions for non self-adjoint perturbations of self-adjoint Berezin-Toeplitz operators of the complex plane. In the second part, we look into quantizations of the torus, namely the Berezin-Toeplitz, the classical Weyl and the complex Weyl quantizations of the torus. We establish links between these different quantizations using Bargmann transform. We propose a conjecture, supported by numerical simulations, on Bohr-Sommerfeld quantization conditions for non self-adjoint perturbations of self-adjoint Berezin-Toeplitz operators of the torus
Vasilyev, Vladimir. "Second-Order Trace Formulas in Szegö-type Theorems." Master's thesis, Universitätsbibliothek Chemnitz, 2007. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200700199.
Full textZabroda, Olga Nikolaievna. "Generalized convolution operators and asymptotic spectral theory." Doctoral thesis, Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200602061.
Full textSeidel, Markus. "Über die Splitting-Eigenschaft der Approximationszahlen von Matrix-Folgen: l1-Theorie." Master's thesis, Universitätsbibliothek Chemnitz, 2007. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200700129.
Full textOrdoñez, Delgado Bartleby. "Algebras de operadores Toeplitz." Bachelor's thesis, Universidad Nacional Mayor de San Marcos, 2015. https://hdl.handle.net/20.500.12672/4344.
Full textIn this work we examine C*-algebras of Toeplitz operators over the unit ball inCn and the unit polydisc in C². Toeplitz operators are interesting examples of non-normal operators that generate non-commutative C*-algebras. Moreover, in the nice cases (depending on the geometry of the domain) of algebras of Toeplitz operators we can recover some analogues of the spectral theorem up to compact operators. In this setting, we can capture the index of a Fredholm operator which is a fundamental numerical invariant in Operator Theory.
Tesis
Ordonez-Delgado, Bartleby. "Algebras of Toeplitz Operators." Thesis, Virginia Tech, 2006. http://hdl.handle.net/10919/32378.
Full textMaster of Science
Gaaya, Haykel. "Inégalités de von Neumann sous contraintes, image numérique de rang supérieur et applications à l’analyse harmonique." Thesis, Lyon 1, 2011. http://www.theses.fr/2011LYO10247/document.
Full textThis thesis joins in the field of operator theory. We are specially interested by the extremal operator S(Φ) defined by the compression of the unilateral shift S to the model subspace H(Φ) where Φ is an inner function on the unit disc. The numerical radius of S(Φ) seems to be important and have many applications to harmonic analysis. C. Badea and G. Cassier showed that there is a relationship between the numerical radius of such operators and the Taylor coefficients of positive rational functions. We give an extension of C. Badea and G. Cassier result and an explicit formula of the numerical radius of S(Φ) in the particular case where Φ is a finite Blaschke product with unique zero. An estimate in the general case is also established. The second part is devoted to the study of the higher rank-k numerical range denoted by Λk(T) which is the set of all complex number λ satisfying PTP = λP for some rank-k orthogonal projection P. This notion was introduced by M.-D. Choi, D. W. Kribs, et K. Zyczkowski motivated by a problem in Physics. We show that if Sn is the n-dimensional shift then its rank-k numerical range is the circular discentered in zero and with a precise radius
Schulze, Bert-Wolfgang, and Nikolai Tarkhanov. "Boundary value problems with Toeplitz conditions." Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2009/2983/.
Full textOrdonez-Delgado, Bartleby. "An Embedded Toeplitz Problem." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/29007.
Full textPh. D.
Axelsson, Andreas, and kax74@yahoo se. "Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces." The Australian National University. School of Mathematical Sciences, 2002. http://thesis.anu.edu.au./public/adt-ANU20050106.093019.
Full textFedchenko, Dmitry, and Nikolai Tarkhanov. "An index formula for Toeplitz operators." Universität Potsdam, 2014. http://opus.kobv.de/ubp/volltexte/2014/7249/.
Full textDeleporte-Dumont, Alix. "Low-energy spectrum of Toeplitz operators." Thesis, Strasbourg, 2019. http://www.theses.fr/2019STRAD004/document.
Full textBerezin-Toeplitz operators allow to quantize functions, or symbols, on compact Kähler manifolds, and are defined using the Bergman (or Szeg\H{o}) kernel. We study the spectrum of Toeplitz operators in an asymptotic regime which corresponds to a semiclassical limit. This study is motivated by the atypic magnetic behaviour observed in certain crystals at low temperature. We study the concentration of eigenfunctions of Toeplitz operators in cases where subprincipal effects (of same order as the semiclassical parameter) discriminate between different classical configurations, an effect known in physics as quantum selection . We show a general criterion for quantum selection and we give detailed eigenfunction expansions in the Morse and Morse-Bott case, as well as in a degenerate case. We also develop a new framework in order to treat Bergman kernels and Toeplitz operators with real-analytic regularity. We prove that the Bergman kernel admits an expansion with exponentially small error on real-analytic manifolds. We also obtain exponential accuracy in compositions and spectra of operators with analytic symbols, as well as exponential decay of eigenfunctions
Nikpour, Mehdi. "Toeplitzness of Composition Operators and Parametric Toeplitzness." University of Toledo / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1346951238.
Full textLangenau, Holger. "Best constants in Markov-type inequalities with mixed weights." Doctoral thesis, Universitätsbibliothek Chemnitz, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-200815.
Full textMarkovungleichungen liefern obere Schranken an die Norm einer (höheren) Ableitung eines algebraischen Polynoms in Bezug auf die Norm des Polynoms selbst. Diese vorliegende Arbeit betrachtet den Fall, dass die Normen vom Laguerre-, Gegenbauer- oder Hermitetyp sind, wobei die entsprechenden Gewichte auf beiden Seiten unterschiedlich gewählt werden. Es wird die kleinste Konstante bestimmt, sodass diese Ungleichung für jedes Polynom vom Grad höchstens n erfüllt ist. Die gesuchte kleinste Konstante kann als die Operatornorm des Differentialoperators dargestellt werden. Diese fällt aber mit der Spektralnorm der Matrixdarstellung in einem Paar geeignet gewählter Orthonormalbasen zusammen und kann daher gut behandelt werden. Zur Abschätzung dieser Normen kommen verschiedene Methoden zum Einsatz, die durch die Differenz der in den Gewichten auftretenden Parameter bestimmt werden. Bis auch eine kleine Lücke im Parameterbereich wird das asymptotische Verhalten der kleinsten Konstanten in jedem der betrachteten Fälle ermittelt
Gaebler, David. "Toeplitz Operators on Locally Compact Abelian Groups." Scholarship @ Claremont, 2004. https://scholarship.claremont.edu/hmc_theses/163.
Full textVasaturo, Anthony P. Vasaturo. "Invertibility of Toeplitz Operators via Berezin Transforms." University of Toledo / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1529951538729292.
Full textBallard, Grey M. "Asymptotic behavior of the eigenvalues of Toeplitz integral operators associated with the Hankel transform." Electronic thesis, 2008. http://dspace.zsr.wfu.edu/jspui/handle/10339/221.
Full textLangenau, Holger. "Best constants in Markov-type inequalities with mixed weights." Doctoral thesis, Universitätsverlag der Technischen Universität Chemnitz, 2015. https://monarch.qucosa.de/id/qucosa%3A20429.
Full textMarkovungleichungen liefern obere Schranken an die Norm einer (höheren) Ableitung eines algebraischen Polynoms in Bezug auf die Norm des Polynoms selbst. Diese vorliegende Arbeit betrachtet den Fall, dass die Normen vom Laguerre-, Gegenbauer- oder Hermitetyp sind, wobei die entsprechenden Gewichte auf beiden Seiten unterschiedlich gewählt werden. Es wird die kleinste Konstante bestimmt, sodass diese Ungleichung für jedes Polynom vom Grad höchstens n erfüllt ist. Die gesuchte kleinste Konstante kann als die Operatornorm des Differentialoperators dargestellt werden. Diese fällt aber mit der Spektralnorm der Matrixdarstellung in einem Paar geeignet gewählter Orthonormalbasen zusammen und kann daher gut behandelt werden. Zur Abschätzung dieser Normen kommen verschiedene Methoden zum Einsatz, die durch die Differenz der in den Gewichten auftretenden Parameter bestimmt werden. Bis auch eine kleine Lücke im Parameterbereich wird das asymptotische Verhalten der kleinsten Konstanten in jedem der betrachteten Fälle ermittelt.
Yousef, Abdelrahman F. "Two problems in the theory of Toeplitz operators on the Bergman space /." Connect to full text in OhioLINK ETD Center, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1242219617.
Full textSubedi, Krishna Subedi. "Hyponormality and Positivity of Toeplitz operators via the Berezin transform." University of Toledo / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1532963068992661.
Full textKraemer, Daniel [Verfasser], and Jörg [Akademischer Betreuer] Eschmeier. "Toeplitz operators on Hardy spaces / Daniel Kraemer ; Betreuer: Jörg Eschmeier." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2020. http://d-nb.info/1209947455/34.
Full textTattersall, Joshua Malcolm. "Toeplitz and Hankel operators on Hardy spaces of complex domains." Thesis, University of Leeds, 2015. http://etheses.whiterose.ac.uk/11498/.
Full textWebb, Marcus David. "Isospectral algorithms, Toeplitz matrices and orthogonal polynomials." Thesis, University of Cambridge, 2017. https://www.repository.cam.ac.uk/handle/1810/264149.
Full textFulsche, Robert [Verfasser]. "Toeplitz operators and generated algebras on non-Hilbertian spaces / Robert Fulsche." Hannover : Gottfried Wilhelm Leibniz Universität, 2020. http://d-nb.info/1223090264/34.
Full textPang, Hong Kui. "New numerical methods and analysis for Toeplitz matrices with financial applications." Thesis, University of Macau, 2011. http://umaclib3.umac.mo/record=b2492157.
Full textFalk, Kevin. "Berezin--Toeplitz quantization and noncommutative geometry." Thesis, Aix-Marseille, 2015. http://www.theses.fr/2015AIXM4033/document.
Full textThe results of this thesis show links between the Berezin--Toeplitz quantization and noncommutative geometry.We first give an overview of the three different domains we handle: the theory of Toeplitz operators (classical and generalized), the geometric and deformation quantizations and the principal tools we use in noncommutative geometry.The first step of the study consists in giving examples of spectral triples (A,H,D) involving algebras of Toeplitz operators acting on the Hardy and weighted Bergman spaces over a smoothly bounded strictly pseudoconvex domain Omega of Cn, and also on the Fock space over Cn. It is shown that resulting noncommutative spaces are regular and of the same dimension as the complex domain. We also give and compare different classes of operator D, first by transporting the usual Dirac operator on L2(Rn) via unitaries, and then by considering the Poisson extension operator or the complex normal derivative on the boundary.Secondly, we show how the Berezin--Toeplitz star product over Omega naturally induces a spectral triple of dimension n+1 whose construction involves sequences of Toeplitz operators over weighted Bergman spaces. This result led us to study more generally to what extent a family of spectral triples can be integrated to form another spectral triple. We also provide an example of such triple
Schulze, Bert-Wolfgang. "Toeplitz operators, and ellipticity of boundary value problems with global projection conditions." Universität Potsdam, 2003. http://opus.kobv.de/ubp/volltexte/2008/2651/.
Full textYousef, Abdelrahman Fawzi. "Two Problems in the Theory of Toeplitz Operators on the Bergman Space." University of Toledo / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1242219617.
Full textRandriamahaleo, Fanilo rajaofetra. "Opérateurs de Toeplitz sur l'espace de Bergman harmonique et opérateurs de Teoplitz tronqués de rang fini." Thesis, Bordeaux, 2015. http://www.theses.fr/2015BORD0108/document.
Full textIn the first part of the thesis,we give some classical results concerning theHardy space, models spaces and analytic and harmonic Bergman spaces. The basic concepts such as projections and reproducing kernels are introduced. We then describe our results on the the stability of the product and the commutativity of two quasihomogeneous Toeplitz operators on the harmonic Bergman space. Finally, we give the matrix description of truncated Toeplitz operators of type "a" in the finite dimensional case
Kou, Kit Ian. "Fast transform based operators for Toeplitz systems and their applications in image restoration." Thesis, University of Macau, 1999. http://umaclib3.umac.mo/record=b1446619.
Full textSchillo, Dominik Tobias [Verfasser], and Jörg [Akademischer Betreuer] Eschmeier. "K-contractions and perturbations of Toeplitz operators / Dominik Tobias Schillo ; Betreuer: Jörg Eschmeier." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2018. http://d-nb.info/1175950130/34.
Full textSchillo, Dominik Tobias Verfasser], and Jörg [Akademischer Betreuer] [Eschmeier. "K-contractions and perturbations of Toeplitz operators / Dominik Tobias Schillo ; Betreuer: Jörg Eschmeier." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2018. http://nbn-resolving.de/urn:nbn:de:bsz:291--ds-275628.
Full textHarutyunyan, Anahit V. "Toeplitz operators and division theorems in anisotropic spaces of holomorphic functions in the polydisc." Universität Potsdam, 2001. http://opus.kobv.de/ubp/volltexte/2008/2611/.
Full textIssa, Hassan A. [Verfasser], Wolfram [Akademischer Betreuer] Bauer, and Ingo [Akademischer Betreuer] Witt. "The analysis of Toeplitz operators, commutative Toeplitz algebras and applications to heat kernel constructions / Hassan A. Issa. Gutachter: Wolfram Bauer ; Ingo Witt. Betreuer: Wolfram Bauer." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2012. http://d-nb.info/1042970947/34.
Full textZhang, Ying Ying. "Preconditioning techniques for a family of Toeplitz-like systems with financial applications." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2151602.
Full textBauer, Wolfram [Verfasser]. "Toeplitz Operators on finite and infinite dimensional spaces with associated Psi*-Fréchet Algebras / Wolfram Bauer." Aachen : Shaker, 2006. http://d-nb.info/1186587393/34.
Full textBogveradze, Giorgi. "Fredholm theory for Wiener-Hopf plus Hankel operators." Doctoral thesis, Universidade de Aveiro, 2008. http://hdl.handle.net/10773/2935.
Full textNa 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.
Le, Floch Yohann. "Théorie spectrale inverse pour les opérateurs de Toeplitz 1D." Phd thesis, Université Rennes 1, 2014. http://tel.archives-ouvertes.fr/tel-01065441.
Full textDetcherry, Renaud. "Analyse semi-classique des opérateurs courbes en TQFT." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066252/document.
Full textIn this thesis we study the asymptotics of some invariants of 3-manifolds, known as "quantum invariants" which were defined by Witten, Reshetikhin and Turaev. These invariants are part of a TQFT structure, that is a monoidal functor for a category of cobordism to the category of complex vector spaces. In this setting, curves on surfaces induce endomorphisms of TQFT vector spaces, called curve operators, which are one of the main object in our study. All these invariants depend of an integer parameter r, and we are interested in their behavior when r tends to infinity. We can then see that quantum invariants are related to more geometric objects, like the moduli space of conjugacy classes of SU2 representations of the fundamental group of a surface. The thesis is divided in 3 parts: in the first one we introduce the notion of TQFT and the Witten-Reshetikhin-Turaev invariants, then we give basic properties of the SU2-moduli spaces and explain the general approach of geometric quantification. In the second one we present a result on the asymptotics of matrix coefficients of curve operators. Using skein calculus and a theorem of Bullock, we express the first two terms of their expansion in terms of trace functions on the SU2-moduli space associated to multicurves. The final part gives an asymptotic expansion of matrix coefficents of quantum representations. A geometric model for TQFT vector spaces is defined, and we show that curve operators can be seen as Toeplitz operators in this model. Standard tools of semi-classical analysis allow us to deduce the result from this
Tytgat, Romaric. "Trace de Dixmier d'opérateurs de Hankel." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4772/document.
Full textWe study Hankel operators $H_{bar{f}}$ with anti holomorphic symbol $bar{f}$ and we are interested to the Dixmier space $mathcal{D}^{p}$ ($pgeq1$), the set of functions $f$ such that $|H_{bar{f}}|^{p} in mathcal{S}^{+}_{1}$ the Macaev ideal. We look Dixmier space as a limit of Schatten class. When $f in mathcal{D}^{p}$, we study $Tr_{omega}(|$H_{bar{f}}$|^{p})$ the Dixmier trace of $|H_{bar{f}}|^{p}$. We have different results when $f$ is an entire or a holomorphic function of the unit disk in the complex plan. We study also the Dixmier space of the little Hankel operator, Toeplitz operator and composition operator