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Relevant bibliographies by topics / Bergman spaces. Toeplitz operators

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Academic literature on the topic 'Bergman spaces. Toeplitz operators'

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Published: 4 June 2021

Last updated: 2 February 2022

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Journal articles on the topic "Bergman spaces. Toeplitz operators"

1

Faour, Nazih S. "Toeplitz operators on Bergman spaces." Rendiconti del Circolo Matematico di Palermo 35, no. 2 (June 1986): 221–32. http://dx.doi.org/10.1007/bf02844733.

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Chacón, Gerardo R. "Toeplitz Operators on Weighted Bergman Spaces." Journal of Function Spaces and Applications 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/753153.

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3

Engliš, Miroslav. "Some density theorems for Toeplitz operators on Bergman spaces." Czechoslovak Mathematical Journal 40, no. 3 (1990): 491–502. http://dx.doi.org/10.21136/cmj.1990.102402.

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Mannersalo, Paula. "Toeplitz operators on Bergman spaces of polygonal domains." Proceedings of the Edinburgh Mathematical Society 62, no. 4 (June 26, 2019): 1115–36. http://dx.doi.org/10.1017/s0013091519000105.

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AbstractWe study the boundedness of Toeplitz operators with locally integrable symbols on Bergman spaces Ap(Ω), 1 < p < ∞, where Ω ⊂ ℂ is a bounded simply connected domain with polygonal boundary. We give sufficient conditions for the boundedness of generalized Toeplitz operators in terms of ‘averages’ of symbol over certain Cartesian squares. We use the Whitney decomposition of Ω in the proof. We also give examples of bounded Toeplitz operators on Ap(Ω) in the case where polygon Ω has such a large corner that the Bergman projection is unbounded.

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STROETHOFF, KAREL. "Compact Toeplitz operators on Bergman spaces." Mathematical Proceedings of the Cambridge Philosophical Society 124, no. 1 (July 1998): 151–60. http://dx.doi.org/10.1017/s0305004197002375.

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Let Bn denote the open unit ball in Cn. We write V to denote Lebesgue volume measure on Bn normalized so that V(Bn)=1. Fix −1<γ<∞ and let Vγ denote the measure given by dVγ(z)=cγ (1−[mid ]z[mid ]2)γdV(z), for z∈Bn, where cγ=Γ(n+γ+1)/ (n!Γ(γ+1)); then Vγ(Bn)=1. The weighted Bergman space A2,γ(Bn) is the space of all analytic functions in L2(Bn, dVγ). This is a closed linear subspace of L2(Bn, dVγ). Let Pγ denote the orthogonal projection of L2(Bn, dVγ) onto A2,γ(Bn). For a function f∈L∞(Bn) the Toeplitz operator Tf is defined on A2,γ(Bn) by Tfh=Pγ(fh), for h∈A2,γ(Bn). It is clear that Tf is bounded on A2,γ(Bn) with ∥Tf∥[les ]∥f∥∞. In this paper we will consider the question for which f∈L∞(Bn) the operator Tf is compact on A2,γ(Bn). Although a complete answer has been given by the author and D. Zheng (see the next section), the condition for compactness is somewhat unnatural. In this article we will give a more natural description for compactness of Toeplitz operators with sufficiently nice symbols. We will describe compactness in terms of behaviour of the so-called Berezin transform of the symbol, which has been useful in characterizing compactness of Toeplitz operators with positive symbols (see [5, 9]). Before we can define this Berezin transform we need to introduce more notation.

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Choe, Boo Rim, Young Joo Lee, and Kyunguk Na. "Toeplitz operators on harmonic Bergman spaces." Nagoya Mathematical Journal 174 (2004): 165–86. http://dx.doi.org/10.1017/s0027763000008837.

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AbstractWe study Toeplitz operators on the harmonic Bergman spaces on bounded smooth domains. Two classes of symbols are considered; one is the class of positive symbols and the other is the class of uniformly continuous symbols. For positive symbols, boundedness, compactness, and membership in the Schatten classes are characterized. For uniformly continuous symbols, the essential spectra are described.

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Miao, Jie. "Toeplitz operators on harmonic Bergman spaces." Integral Equations and Operator Theory 27, no. 4 (December 1997): 426–38. http://dx.doi.org/10.1007/bf01192123.

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Chailuek, Kamthorn, and Brian C. Hall. "Toeplitz Operators on Generalized Bergman Spaces." Integral Equations and Operator Theory 66, no. 1 (January 2010): 53–77. http://dx.doi.org/10.1007/s00020-009-1734-6.

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9

Elias, Norma. "Toeplitz operators on weighted Bergman spaces." Integral Equations and Operator Theory 11, no. 3 (May 1988): 310–31. http://dx.doi.org/10.1007/bf01202076.

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Stroethoff, Karel. "Compact Toeplitz operators on weighted harmonic Bergman spaces." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 64, no. 1 (February 1998): 136–48. http://dx.doi.org/10.1017/s144678870000135x.

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AbstractWe consider the Bergman spaces consisting of harmonic functions on the unit ball in Rn that are squareintegrable with respect to radial weights. We will describe compactness for certain classes of Toeplitz operators on these harmonic Bergman spaces.

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Dissertations / Theses on the topic "Bergman spaces. Toeplitz operators"

1

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.

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Arroussi, Hicham. "Function and Operator Theory on Large Bergman spaces." Doctoral thesis, Universitat de Barcelona, 2016. http://hdl.handle.net/10803/395175.

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The theory of Bergman spaces has been a central subject of study in complex analysis during the past decades. The book [7] by S. Bergman contains the first systematic treat-ment of the Hilbert space of square integrable analytic functions with respect to Lebesgue area measure on a domain. His approach was based on a reproducing kernel that became known as the Bergman kernel function. When attention was later directed to the spaces AP over the unit disk, it was natural to call them Bergman spaces. As counterparts of Hardy spaces, they presented analogous problems. However, although many problems in Hardy spaces were well understood by the 1970s, their counterparts for Bergman spaces were generally viewed as intractable, and only some isolated progress was done. The 1980s saw the emerging of operator theoretic studies related to Bergman spaces with important contributions by several authors. Their achievements on Bergman spaces with standard weights are presented in Zhu's book [77]. The main breakthroughs came in the 1990s, where in a flurry of important advances, problems previously considered intractable began to be solved. First came Hedenmalm's construction of canonical divisors [26], then Seip's description [59] of sampling and interpolating sequences on Bergman spaces, and later on, the study of Aleman, Richter and Sundberg [1] on the invariant subspaces of A2, among others. This attracted other workers to the field and inspired a period of intense research on Bergman spaces and related topics. Nowadays there are rich theories on Bergman spaces that can be found on the textbooks [27] and [22]. Meanwhile, also in the nineties, some isolated problems on Bergman spaces with ex-ponential type weights began to be studied. These spaces are large in the sense that they contain all the Bergman spaces with standard weights, and their study presented new dif-ficulties, as the techniques and ideas that led to success when working on the analogous problems for standard Bergman spaces, failed to work on that context. It is the main goal of this work to do a deep study of the function theoretic properties of such spaces, as well as of some operators acting on them. It turns out that large Bergman spaces are close in spirit to Fock spaces [79], and many times mixing classical techniques from both Bergman and Fock spaces in an appropriate way, can led to some success when studying large Bergman spaces.

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Randriamahaleo, 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.

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Dans la première partie de la thèse, nous donnons les résultats classiques concernant l’espace de Hardy, les espaces modèles et les espaces de Bergman analytique et harmonique. Les notions de base telles que les projections et les noyaux reproduisant y sont introduites. Nous exposons ensuite nos résultats concernant d’une part, la stabilité du produit et la commutativité de deux opérateurs de Toeplitz quasihomogènes et d’autre part, la description matricielle des opérateurs de Toeplitz tronqués du type "a" "dans le cas de la dimension finie
In 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

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Yousef, 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.

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Subedi, 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.

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Le, Van An. "Petits espaces de Fock, petits espaces de Bergman et leurs opérateurs." Thesis, Aix-Marseille, 2019. http://theses.univ-amu.fr.lama.univ-amu.fr/191210_LE_604try554eejyoj865ovdfq987fxy_TH.pdf.

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Nous étudions les mesures de Carleson et les opérateurs de Toeplitz sur la classe des espaces de Bergman dite de petite taille, introduits récemment par Seip. On obtient une caractérisation des mesures de Carleson qui étend les résultats de Seip à partir du disque unité de mathbb C à la boule unité mathbb Bn de mathbb Cn. Nous utilisons cette caractérisation pour donner les conditions nécessaires et suffisantes à la continuité et à la compacité des opérateurs de Toeplitz. Enfin, nous étudions l’appartenance des opérateurs Toeplitz aux classes de Schatten d'ordre p pour 1
We study the Carleson measures and the Toeplitz operators on the class of the so-called small weighted Bergman spaces, introduced recently by Seip. A characterization of Carleson measures is obtained which extends Seip's results from the unit disk of mathbb C to the unit ball mathbb Bn of mathbb Cn. We use this characterization to give necessary and sufficient conditions for the boundedness and compactness of Toeplitz operators. Finally, we study the Schatten p classes membership of Toeplitz operators for 1

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Jones, Matthew Michael. "Composition operators on weighted Bergman spaces." Thesis, University College London (University of London), 1999. http://discovery.ucl.ac.uk/1363351/.

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In the late 1960’s, E.A. Nordgren and J.V. Ryff studied composition operators on the Hardy space H2. They provided upper and lower bounds on the norms of general composition operators and gave the exact norm in the case where the symbol map is an inner function. Composition operators themselves, on various other spaces, have been studied by many authors since and much deep work has been done concerning them. Recently, however B.D. MacCluer and T. Kriete have developed the study of composition operators on very general weighted Bergman spaces of the unit disk in the complex plane. My starting point is this work. Composition operators serve well to link the two areas of analysis, operator theory and complex function theory. The products of this link lie deep in complex analysis and are diverse indeed. These include a thorough study of the Schr¨oeder functional equation and its solutions, see [16] and the references therein, in fact some of the well known conjectures can be linked to composition operators. Nordgren, [12], has shown that the Invariant Subspace Problem can be solved by classifying the minimal invariant subspaces of a certain composition operator on H2, and de Branges used composition operators to prove the Bieberbach conjecture. In this thesis, I use various methods from complex function theory to prove results concerning composition operators on weighted Bergman spaces of the unit disk, the main result is the confirmation of two conjectures of T. Kriete, which appeared in [7]. I also construct, in the final chapter, inner functions which map one arbitrary weighted Bergman space into another.

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Oliver, Vendrell Roc. "Hankel operators on vector-valued Bergman spaces." Doctoral thesis, Universitat de Barcelona, 2017. http://hdl.handle.net/10803/471520.

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The main goal of this work is to study vector-valued Bergman spaces and to obtain the weak factorization of these spaces. In order to do that we need to study small Hankel operators with operator-valued holomorphic symbols. We also study the big Hankel operator acting on vector-valued Bergman spaces. In Chapter 1 we collect all the previous results and notations needed to follow the rest of the manuscript. More concretely, some of the topics covered in this chapter are the Bochner integral, the integral for vector-valued functions appearing first in Bochner; the Bergman metric, results of the metric used in Bn; harmonic and subharmonic function; basic notions of differentiation, where the differential operators R(a, t) are presented which is important in the next chapters and in the final section we recall some topics on Banach spaces, as the Rademacher type and cotype of a Banach space and some other related results. Having all that in mind, in Chapter 2, the vector-valued Bergman spaces are presented. The vector-valued Bloch type spaces play a similar role and therefore we dedícate one full chapter to these spaces. Chapter 3 is devoted to present and characterize the vector-valued Bloch type spaces. Since we mention Hankel operators, in Chapter 4 we prove the characterization of the boundedness of the small Hankel operator with analytic operator-valued symbols between vector-valued Bergman spaces (of different type). We explain what this means in the following. Another very important consequence of the boundedness of the small Hankel operator between vector-valued Bergman spaces is shown in Chapter 5. We establish the weak factorization of the vector-valued Bergman spaces. Factorization of analytic functions is a very big topic and many people worked on it during many years and it is known to have many applications. Therefore, in Chapter 6 we fully characterize the boundedness of the big Hankel operator on vector-valued Bergman spaces in terms of its operator-valued holomorphic symbol for all cases of p > 1 and q > 1, and so we solve and generalize the previous problem. Finally, in Chapter 7 we discuss some open problems we have not been able to solve, as well as some other interesting problems in the same line as this work in order to look on the future.

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9

Kraemer, 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.

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Tattersall, Joshua Malcolm. "Toeplitz and Hankel operators on Hardy spaces of complex domains." Thesis, University of Leeds, 2015. http://etheses.whiterose.ac.uk/11498/.

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The major focus is on the Hardy spaces of the annulus {z : s < |z| < 1}, with the measure on the boundary being Lebesgue measure normalised such that each boundary has weight 1. There is also consideration of higher order annuli, the Bergmann spaces and slit domains. The focus was on considering analogues of classical problems in the disc in multiply connected regions. Firstly, a few factorisation results are established that will assist in later chapters. The Douglas-Rudin type factorisation is an analogue of factorisation in the disc, and the factorisation of H1 into H2 functions are analogues of factorisation in the disc, whereas the multiplicative factorisation is specific to multiply connected domains. The Douglas-Rudin type factorisation is a classical result for the Hardy space of the disc, here it is shown for the domain {z : s < |z| < 1}. A previous factorisation for H1 into H2 functions exists in [4], an improved constant not depending on s is found here. We proceed to investigate real-valued Toeplitz operators in the annulus, focusing on eigenvalues and eigenfunctions, including for higher order annuli, and amongst other results the general form of an eigenfunction is determined. A paper of Broschinski [10] details the same approach for the annulus {z : s < |z| < 1} as here, but does not consider higher genus settings. There exists work such as in [6] and [5] detailing an alternative approach to eigenvalues in a general setting, using theta-functions, and does not detail the eigenfunctions. After this, kernels of a more general symbol are considered, compared to the disc, and Dyakanov’s theorem from the disc is extended for the annulus. Hankel operators are also considered, in particular with regards to optimal symbols. Finally, analogues of results from previous chapters are considered in the Bergman space, and the Hardy space of a slit annulus.

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Books on the topic "Bergman spaces. Toeplitz operators"

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Commutative algebras of Toeplitz operators on the Bergman space. Basel: Birkhäuser, 2008.

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2

The bilateral Bergman shift. Providence, R.I., USA: American Mathematical Society, 1986.

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3

Operator theory in function spaces. New York: M. Dekker, 1990.

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Peláez, José Ángel. Weighted Bergman spaces induced by rapidly increasing weights. Providence, Rhode Island: American Mathematical Society, 2014.

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Clay Mathematics Institute Workshop on Moduli Spaces of Vector Bundles, with a View toward Coherent Sheaves (2006 Cambridge, Mass.). Grassmannians, moduli spaces, and vector bundles: Clay Mathematics Institute Workshop on Moduli Spaces of Vector Bundles, with a View towards Coherent Sheaves, October 6-11, 2006, Cambridge, Massachusetts. Edited by Ellwood D. (David) 1966- and Previato Emma. Providence, RI: American Mathematical Society, 2011.

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Regularised integrals, sums, and traces: An analytic point of view. Providence, R.I: American Mathematical Society, 2012.

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Commutative Algebras of Toeplitz Operators on the Bergman Space. Basel: Birkhäuser Basel, 2008. http://dx.doi.org/10.1007/978-3-7643-8726-6.

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Operator Theory in Function Spaces (Mathematical Surveys and Monographs). 2nd ed. American Mathematical Society, 2007.

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Book chapters on the topic "Bergman spaces. Toeplitz operators"

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Zhu, Kehe. "Toeplitz operators on the Bergman space." In Mathematical Surveys and Monographs, 163–206. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/surv/138/07.

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Vasilevski, Nikolai. "Toeplitz Operators on the Bergman Space." In Factorization, Singular Operators and Related Problems, 315–33. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0227-0_21.

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Rozenblum, Grigori, and Nikolai Vasilevski. "Toeplitz Operators with Singular Symbols in Polyanalytic Bergman Spaces on the Half-Plane." In Operator Algebras, Toeplitz Operators and Related Topics, 403–21. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44651-2_23.

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Sánchez-Nungaray, Armando, and Nikolai Vasilevski. "Toeplitz Operators on the Bergman Spaces with Pseudodifferential Defining Symbols." In Operator Theory, Pseudo-Differential Equations, and Mathematical Physics, 355–74. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0537-7_18.

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Ramírez-Mora, María del Rosario, Josué Ramírez-Ortega, and Miguel Antonio Morales-Ramos. "Algebra Generated by a Finite Number of Toeplitz Operators with Homogeneous Symbols Acting on the Poly-Bergman Spaces." In Operator Algebras, Toeplitz Operators and Related Topics, 383–402. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44651-2_22.

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Rozenblum, Grigori. "Finite Rank Toeplitz Operators in the Bergman Space." In Around the Research of Vladimir Maz'ya III, 331–58. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-1-4419-1345-6_12.

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Vasilevski, N. L. "Bergman Space on Tube Domains and Commuting Toeplitz Operators." In Proceedings of the Second ISAAC Congress, 1523–37. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4613-0271-1_73.

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Zhao, Xianfeng, and Dechao Zheng. "Toeplitz Operators on the Bergman Space and the Berezin Transform." In Handbook of Analytic Operator Theory, 287–318. Boca Raton : CRC Press, Taylor & Francis Group, 2019.: Chapman and Hall/CRC, 2019. http://dx.doi.org/10.1201/9781351045551-10.

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Loaiza, Maribel, and Nikolai Vasilevski. "Toeplitz Operators on the Harmonic Bergman Space with Pseudodifferential Defining Symbols." In Trends in Mathematics, 591–603. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-12577-0_65.

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Böttcher, Albrecht, and Antti Perälä. "The Index Formula of Douglas for Block Toeplitz Operators on the Bergman Space of the Ball." In Operator Theory, Pseudo-Differential Equations, and Mathematical Physics, 39–55. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0537-7_3.

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Conference papers on the topic "Bergman spaces. Toeplitz operators"

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de Fabritiis, Chiara. "Linear Operators on Generalized Bergman Spaces." In GLOBAL ANALYSIS AND APPLIED MATHEMATICS: International Workshop on Global Analysis. AIP, 2004. http://dx.doi.org/10.1063/1.1814725.

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REHBERG, BETTINA. "HANKEL OPERATORS ON GENERALIZED BERGMAN-HARDY SPACES." In Proceedings of the Tenth General Meeting. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704276_0021.

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Vasilevski, Nikolai, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Two-dimensional Singular Integral Operators via Poly-Bergman Spaces." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3637754.

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ZORBOSKA, N. "MULTIPLICATION AND TOEPLITZ OPERATORS ON THE ANALYTIC BESOV SPACES." In Proceedings of the 5th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812835635_0036.

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LI, SONG-YING. "ON THE CRITERIA FOR SCHATTEN VON NEUMANN CLASS COMPOSITION OPERATORS ON HARDY AND BERGMAN SPACES IN DOMAINS IN ℂN." In Proceedings of a Satellite Conference to the International Congress of Mathematicians in Beijing 2002. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702500_0015.

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