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Journal articles on the topic 'Fredholm theory'

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Published: 4 June 2021
Last updated: 29 January 2023

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Benjamin, Ronalda, and Sonja Mouton. "Fredholm theory in ordered Banach algebras." Quaestiones Mathematicae 39, no. 5 (July 18, 2016): 643–64. http://dx.doi.org/10.2989/16073606.2016.1167134.

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12

Aiena, Pietro. "On the Fredholm theory of multipliers." Proceedings of the American Mathematical Society 120, no. 1 (January 1, 1994): 89. http://dx.doi.org/10.1090/s0002-9939-1994-1145939-4.

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13

Hofer, H. "A General Fredholm Theory and Applications." Current Developments in Mathematics 2004, no. 1 (2004): 1–72. http://dx.doi.org/10.4310/cdm.2004.v2004.n1.a1.

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14

Alvarez, Teresa, and Manuel González. "Paracomplete normed spaces and Fredholm theory." Rendiconti del Circolo Matematico di Palermo 48, no. 2 (June 1999): 257–64. http://dx.doi.org/10.1007/bf02857302.

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15

Tajmouati, Abdelaziz, Mohamed Amouch, and Mohammed Karmouni. "Symmetric difference between pseudo B-Fredholm spectrum and spectra originated from fredholm theory." Filomat 31, no. 16 (2017): 5057–64. http://dx.doi.org/10.2298/fil1716057t.

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In this paper, we continue the study of the pseudo B-Fredholm operators of Boasso, and the pseudo B-Weyl spectrum of Zariouh and Zguitti; in particular we find that the pseudo B-Weyl spectrum is empty whenever the pseudo B-Fredholm spectrum is, and look at the symmetric differences between the pseudo B-Weyl and other spectra.
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16

Dont, Miroslav, and Eva Dontová. "Invariance of the Fredholm radius of an operator in potential theory." Časopis pro pěstování matematiky 112, no. 3 (1987): 269–83. http://dx.doi.org/10.21136/cpm.1987.118323.

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17

Li, Weiping, and Shuguang Wang. "INSTANTONS ON CONIC 4-MANIFOLDS: FREDHOLM THEORY." Journal of the Korean Mathematical Society 44, no. 2 (March 31, 2007): 275–96. http://dx.doi.org/10.4134/jkms.2007.44.2.275.

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18

González, Manuel, Fernando León-Saavedra, and Alfonso Montes-Rodríguez. "Semi-Fredholm Theory: Hypercyclic and Supercyclic Subspaces." Proceedings of the London Mathematical Society 81, no. 1 (July 2000): 169–89. http://dx.doi.org/10.1112/s0024611500012454.

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19

Ivković, Stefan. "Semi-Fredholm theory on Hilbert $C^{*}$ -modules." Banach Journal of Mathematical Analysis 13, no. 4 (October 2019): 989–1016. http://dx.doi.org/10.1215/17358787-2019-0022.

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20

González, Manuel. "The perturbation classes problem in Fredholm theory." Journal of Functional Analysis 200, no. 1 (May 2003): 65–70. http://dx.doi.org/10.1016/s0022-1236(02)00071-x.

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21

De Grande-De Kimpe, N., and J. Martinez-Maurica. "Fredholm theory forp-adic locally convex spaces." Annali di Matematica Pura ed Applicata 160, no. 1 (December 1991): 223–34. http://dx.doi.org/10.1007/bf01764129.

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22

Schmoeger, Christoph. "SEMI-FREDHOLM OPERATORS AND LOCAL SPECTRAL THEORY." Demonstratio Mathematica 28, no. 4 (October 1, 1995): 997–1004. http://dx.doi.org/10.1515/dema-1995-0426.

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23

Eschmeier, Jörg. "Grothendieck’s comparison theorem and multivariable Fredholm theory." Archiv der Mathematik 92, no. 5 (April 24, 2009): 461–75. http://dx.doi.org/10.1007/s00013-009-3173-7.

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24

Benjamin, Ronalda, and Sonja Mouton. "r-Fredholm theory in ordered Banach algebras." Positivity 24, no. 2 (June 25, 2019): 373–93. http://dx.doi.org/10.1007/s11117-019-00683-3.

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25

Lukoto, Tshikhudo, and Heinrich Raubenheimer. "Perturbation Ideals and Fredholm Theory in Banach Algebras." Extracta Mathematicae 37, no. 1 (June 1, 2022): 91–110. http://dx.doi.org/10.17398/2605-5686.37.1.91.

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26

An, Il, and Jaeseong Heo. "Weyl type theorems for selfadjoint operators on Krein spaces." Filomat 32, no. 17 (2018): 6001–16. http://dx.doi.org/10.2298/fil1817001a.

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In this paper, we introduce a notion of the J-kernel of a bounded linear operator on a Krein space and study the J-Fredholm theory for Krein space operators. Using J-Fredholm theory, we discuss when (a-)J-Weyl?s theorem or (a-)J-Browder?s theorem holds for bounded linear operators on a Krein space instead of a Hilbert space.
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27

Kaad, J. "Comparison of secondary invariants of algebraic K-theory." Journal of K-Theory 8, no. 1 (July 21, 2010): 169–82. http://dx.doi.org/10.1017/is010006019jkt119.

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28

MICKELSSON, JOUKO. "FAMILIES OF DIRAC OPERATORS AND QUANTUM AFFINE GROUPS." Journal of the Australian Mathematical Society 90, no. 2 (April 2011): 213–20. http://dx.doi.org/10.1017/s1446788711001224.

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AbstractTwisted K-theory classes over compact Lie groups can be realized as families of Fredholm operators using the representation theory of loop groups. In this paper we show how to deform the Fredholm family in the sense of quantum groups. The family of Dirac-type operators is parametrized by vectors in the adjoint module for a quantum affine algebra and transforms covariantly under a central extension of the algebra.
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29

Zhao, Limian, Shanhe Wu, and Wu-Sheng Wang. "A Generalized Nonlinear Volterra-Fredholm Type Integral Inequality and Its Application." Journal of Applied Mathematics 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/865136.

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We establish a new nonlinear retarded Volterra-Fredholm type integral inequality. The upper bounds of the embedded unknown functions are estimated explicitly by using the theory of inequality and analytic techniques. Moreover, an application of our result to the retarded Volterra-Fredholm integral equations for estimation is given.
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30

Král, Josef, and Wolfgang Wendland. "Some examples concerning applicability of the Fredholm-Radon method in potential theory." Applications of Mathematics 31, no. 4 (1986): 293–308. http://dx.doi.org/10.21136/am.1986.104208.

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31

Mickelsson, Jouko. "3D Current Algebra and Twisted K Theory." Reviews in Mathematical Physics 30, no. 07 (July 25, 2018): 1840011. http://dx.doi.org/10.1142/s0129055x18400111.

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Equivariant twisted K theory classes on compact Lie groups [Formula: see text] can be realized as families of Fredholm operators acting in a tensor product of a fermionic Fock space and a representation space of a central extension of the loop algebra [Formula: see text] using a supersymmetric Wess–Zumino–Witten model. The aim of the present paper is to extend the construction to higher loop algebras using an abelian extension of a 3D current algebra. We have only partial success: Instead of true Fredholm operators we have formal algebraic expressions in terms of the generators of the current algebra and an infinite dimensional Clifford algebra. These give rise to sesquilinear forms in a Hilbert bundle which transform in the expected way with respect to 3D gauge transformations but do not define true Hilbert space operators.
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32

Lo, Ching-On, and Anthony Wai-Keung Loh. "Fredholm weighted composition operators." Operators and Matrices, no. 1 (2019): 169–86. http://dx.doi.org/10.7153/oam-2019-13-10.

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33

Takagi, Hiroyuki. "Fredholm weighted composition operators." Integral Equations and Operator Theory 16, no. 2 (June 1993): 267–76. http://dx.doi.org/10.1007/bf01358956.

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34

Zorboska, Nina. "Fredholm and Semi-Fredholm Composition Operators on the Small Bloch-type Spaces." Integral Equations and Operator Theory 75, no. 4 (February 12, 2013): 559–71. http://dx.doi.org/10.1007/s00020-013-2042-8.

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35

BERTOLA, M., and M. CAFASSO. "THE GAP PROBABILITIES OF THE TACNODE, PEARCEY AND AIRY POINT PROCESSES, THEIR MUTUAL RELATIONSHIP AND EVALUATION." Random Matrices: Theory and Applications 02, no. 02 (April 2013): 1350003. http://dx.doi.org/10.1142/s2010326313500032.

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We express the gap probabilities of the tacnode process as the ratio of two Fredholm determinants; the denominator is the standard Tracy–Widom distribution, while the numerator is the Fredholm determinant of a very explicit kernel constructed with Airy functions and exponentials. The formula allows us to apply the theory of numerical evaluation of Fredholm determinants and thus produce numerical results for the gap probabilities. In particular we investigate numerically how, in different regimes, the Pearcey process degenerates to the Airy one, and the tacnode degenerates to the Pearcey and Airy ones.
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36

Mouton, T., and H. Raubenheimer. "FREDHOLM THEORY RELATIVE TO TWO BANACH ALGEBRA HOMOMORPHISMS." Quaestiones Mathematicae 14, no. 4 (October 1991): 371–82. http://dx.doi.org/10.1080/16073606.1991.9631656.

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37

Ruelle, David. "An extension of the theory of Fredholm determinants." Publications mathématiques de l'IHÉS 72, no. 1 (December 1990): 175–93. http://dx.doi.org/10.1007/bf02699133.

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38

Baklouti, Hamadi. "T-Fredholm analysis and application to operator theory." Journal of Mathematical Analysis and Applications 369, no. 1 (September 2010): 283–89. http://dx.doi.org/10.1016/j.jmaa.2010.03.031.

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39

Álvarez, T. "Pseudo B-Fredholm linear relations and spectral theory." Monatshefte für Mathematik 185, no. 4 (October 23, 2017): 541–55. http://dx.doi.org/10.1007/s00605-017-1122-2.

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40

Hofer, Helmut, Krzysztof Wysocki, and Eduard Zehnder. "A General Fredholm Theory II: Implicit Function Theorems." Geometric and Functional Analysis 19, no. 1 (April 28, 2009): 206–93. http://dx.doi.org/10.1007/s00039-009-0715-x.

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41

Filippenko, Benjamin, Zhengyi Zhou, and Katrin Wehrheim. "Counterexamples in scale calculus." Proceedings of the National Academy of Sciences 116, no. 18 (April 12, 2019): 8787–97. http://dx.doi.org/10.1073/pnas.1811701116.

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We construct counterexamples to classical calculus facts such as the inverse and implicit function theorems in scale calculus—a generalization of multivariable calculus to infinite-dimensional vector spaces, in which the reparameterization maps relevant to symplectic geometry are smooth. Scale calculus is a corner stone of polyfold theory, which was introduced by Hofer, Wysocki, and Zehnder as a broadly applicable tool for regularizing moduli spaces of pseudoholomorphic curves. We show how the novel nonlinear scale-Fredholm notion in polyfold theory overcomes the lack of implicit function theorems, by formally establishing an often implicitly used fact: The differentials of basic germs—the local models for scale-Fredholm maps—vary continuously in the space of bounded operators when the base point changes. We moreover demonstrate that this continuity holds only in specific coordinates, by constructing an example of a scale-diffeomorphism and scale-Fredholm map with discontinuous differentials. This justifies the high technical complexity in the foundations of polyfold theory.
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42

Brahim, Fatma, Aref Jeribi, and Bilel Krichen. "Spectral theory for polynomially demicompact operators." Filomat 33, no. 7 (2019): 2017–30. http://dx.doi.org/10.2298/fil1907017b.

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In this article, we introduce the notion of polynomial demicompactness and we use it to give some results on Fredholm operators and to establish a fine description of some essential spectra of a closed densely defined linear operator. Our work is a generalization of many known ones in the literature.
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43

Tian, Yazhou, A. A. El-Deeb, and Fanwei Meng. "Some Nonlinear Delay Volterra–Fredholm Type Dynamic Integral Inequalities on Time Scales." Discrete Dynamics in Nature and Society 2018 (August 12, 2018): 1–8. http://dx.doi.org/10.1155/2018/5841985.

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We are devoted to studying a class of nonlinear delay Volterra–Fredholm type dynamic integral inequalities on time scales, which can provide explicit bounds on unknown functions. The obtained results can be utilized to investigate the qualitative theory of nonlinear delay Volterra–Fredholm type dynamic equations. An example is also presented to illustrate the theoretical results.
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44

Nishioka, Kumiko. "Algebraic independence of Fredholm series." Acta Arithmetica 100, no. 4 (2001): 315–27. http://dx.doi.org/10.4064/aa100-4-2.

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45

Venugopalan, Sushmita, and Guangbo Xu. "Local model for moduli space of affine vortices." International Journal of Mathematics 29, no. 03 (March 2018): 1850020. http://dx.doi.org/10.1142/s0129167x18500209.

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We show that the moduli space of regular affine vortices, which are solutions of the symplectic vortex equation over the complex plane, has the structure of a smooth manifold. The construction uses Ziltener’s Fredholm theory results [A Quantum Kirwan Map: Bubbling and Fredholm Theory, Memiors of the American Mathematical Society, Vol. 230 (American Mathematical Society, Providence, RI, 2014), pp. 1–129]. We also extend the result to the case of affine vortices over the upper half plane. These results are necessary ingredients in defining the “open quantum Kirwan map” proposed by Woodward [Gauged Floer theory for toric moment fibers, Geom. Funct. Anal. 21 (2011) 680–749].
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46

Krushkal, Samuel. "Fredholm eigenvalues and quasiconformal geometry of polygons." Ukrainian Mathematical Bulletin 17, no. 3 (September 17, 2020): 325–64. http://dx.doi.org/10.37069/1810-3200-2020-17-3-3.

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An important open problem in geometric complex analysis is to establish algorithms for the explicit determination of the basic curvilinear and analytic functionals intrinsically connected with conformal and quasiconformal maps, such as their Teichmüller and Grunsky norms, Fredholm eigenvalues, and the quasireflection coefficient. This is important also for the potential theory but has not been solved even for convex polygons. This case has intrinsic interest in view of the connection of polygons with the geometry of the universal Teichmüller space and approximation theory. This survey extends our previous survey of 2005 and presents the newapproaches and recent essential progress in this field of geometric complex analysis and potential theory, having various important applications. Another new topic concerns quasireflections across finite collections of quasiintervals (to which the notion of Fredholm eigenvalues also can be extended).
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47

Krushkal, Samuel. "Fredholm eigenvalues and quasiconformal geometry of polygons." Ukrainian Mathematical Bulletin 17, no. 3 (September 17, 2020): 325–64. http://dx.doi.org/10.37069/1810-3200-2020-17-3-3.

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An important open problem in geometric complex analysis is to establish algorithms for the explicit determination of the basic curvilinear and analytic functionals intrinsically connected with conformal and quasiconformal maps, such as their Teichmüller and Grunsky norms, Fredholm eigenvalues, and the quasireflection coefficient. This is important also for the potential theory but has not been solved even for convex polygons. This case has intrinsic interest in view of the connection of polygons with the geometry of the universal Teichmüller space and approximation theory. This survey extends our previous survey of 2005 and presents the newapproaches and recent essential progress in this field of geometric complex analysis and potential theory, having various important applications. Another new topic concerns quasireflections across finite collections of quasiintervals (to which the notion of Fredholm eigenvalues also can be extended).
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48

Karmouni, Mohammed, and Abdelaziz Tajmouati. "A new characterization of Browder’s theorem." Filomat 32, no. 14 (2018): 4865–73. http://dx.doi.org/10.2298/fil1814865k.

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49

Vougalter, Vitali, and Vitaly Volpert. "Solvability conditions for some non-Fredholm operators." Proceedings of the Edinburgh Mathematical Society 54, no. 1 (November 30, 2010): 249–71. http://dx.doi.org/10.1017/s0013091509000236.

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AbstractWe obtain solvability conditions for some elliptic equations involving non-Fredholm operators with the methods of spectral theory and scattering theory for Schrödinger-type operators. One of the main results of the paper concerns solvability conditions for the equation –Δu+V(x)u–au=fwhere a ≥ 0. The conditions are formulated in terms of orthogonality of the functionfto the solutions of the homogeneous adjoint equation.
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50

Boua, Hamid. "Spectral Theory For Strongly Continuous Cosine." Concrete Operators 8, no. 1 (January 1, 2021): 40–47. http://dx.doi.org/10.1515/conop-2020-0110.

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Abstract Let (C(t)) t∈ℝ be a strongly continuous cosine family and A be its infinitesimal generator. In this work, we prove that, if C(t) – cosh λt is semi-Fredholm (resp. semi-Browder, Drazin inversible, left essentially Drazin and right essentially Drazin invertible) operator and λt ∉ iπℤ, then A – λ 2 is also. We show by counterexample that the converse is false in general.
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