Relevant bibliographies by topics / Bergman spaces

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Bergman spaces'

Author: Grafiati
Published: 4 June 2021
Last updated: 10 March 2023

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Journal articles on the topic "Bergman spaces"

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Alhami, Kifah Y. "OPERATORS ON BERGMAN SPACES." Journal of Southwest Jiaotong University 56, no. 5 (October 30, 2021): 399–403. http://dx.doi.org/10.35741/issn.0258-2724.56.5.35.

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Bergman space theory has been at the core of complex analysis research for many years. Indeed, Hardy spaces are related to Bergman spaces. The popularity of Bergman spaces increased when functional analysis emerged. Although many researchers investigated the Bergman space theory by mimicking the Hardy space theory, it appeared that, unlike their cousins, Bergman spaces were more complex in different aspects. The issue of invariant subspace constitutes one common problem in mathematics that is yet to be resolved. For Hardy spaces, each invariant subspace for shift operators features an elegant description. However, the method for formulating particular structures for the large invariant subspace of shift operators upon Bergman spaces is still unknown. This paper aims to characterize bounded Hankel operators involving a vector-valued Bergman space compared to other different vector value Bergman spaces.
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Reséndis O., L. F., and L. M. Tovar S. "Bicomplex Bergman and Bloch spaces." Arabian Journal of Mathematics 9, no. 3 (July 1, 2020): 665–79. http://dx.doi.org/10.1007/s40065-020-00285-y.

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Abstract In this article, we define the bicomplex weighted Bergman spaces on the bidisk and their associated weighted Bergman projections, where the respective Bergman kernels are determined. We study also the bicomplex Bergman projection onto the bicomplex Bloch space.
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Ghiloufi, N., and M. Zaway. "Meromorphic Bergman spaces." Ukrains’kyi Matematychnyi Zhurnal 74, no. 8 (October 4, 2022): 1060–72. http://dx.doi.org/10.37863/umzh.v74i8.6163.

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UDC 517.5We introduce new spaces of holomorphic functions on the pointed unit disc in <em>C</em> that generalize classical Bergman spaces. We prove some fundamental properties of these spaces and their dual spaces. Finally, we extend the Hardy – Littlewood and Fejer – Riesz inequalities to these spaces with application of the Toeplitz operators. ´
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Vasilevski1, N. L. "On quaternionic bergman and poly-bergman spaces." Complex Variables, Theory and Application: An International Journal 41, no. 2 (April 2000): 111–32. http://dx.doi.org/10.1080/17476930008815241.

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Shamoyan, Romi F., and Olivera Mihić. "On Extremal Problems in Certain New Bergman Type Spaces in Some Bounded Domains inCn." Journal of Function Spaces 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/975434.

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Based on recent results on boundedness of Bergman projection with positive Bergman kernel in analytic spaces in various types of domains inCn, we extend our previous sharp results on distances obtained for analytic Bergman type spaces in unit disk to some new Bergman type spaces in Lie ball, bounded symmetric domains of tube type, Siegel domains, and minimal bounded homogeneous domains.
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Peláez, José Ángel, Jouni Rättyä, and Kian Sierra. "Embedding Bergman spaces into tent spaces." Mathematische Zeitschrift 281, no. 3-4 (September 19, 2015): 1215–37. http://dx.doi.org/10.1007/s00209-015-1528-2.

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Shamoyan, Romi F., and Olivera R. Mihić. "On some extremal problems in Bergman spaces in weakly pseudoconvex domains." Communications in Mathematics 26, no. 2 (December 1, 2018): 83–97. http://dx.doi.org/10.2478/cm-2018-0006.

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AbstractWe consider and solve extremal problems in various bounded weakly pseudoconvex domains in ℂn based on recent results on boundedness of Bergman projection with positive Bergman kernel in Bergman spaces $A_\alpha ^p$ in such type domains. We provide some new sharp theorems for distance function in Bergman spaces in bounded weakly pseudoconvex domains with natural additional condition on Bergman representation formula.
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Axler, Sheldon. "Zero Multipliers of Bergman Spaces." Canadian Mathematical Bulletin 28, no. 2 (June 1, 1985): 237–42. http://dx.doi.org/10.4153/cmb-1985-029-1.

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Lusky, Wolfgang. "On generalized Bergman spaces." Studia Mathematica 119, no. 1 (1996): 77–95. http://dx.doi.org/10.4064/sm-119-1-77-95.

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Rochberg, Richard. "Book Review: Bergman spaces." Bulletin of the American Mathematical Society 42, no. 02 (January 12, 2005): 251–57. http://dx.doi.org/10.1090/s0273-0979-05-01046-3.

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Dissertations / Theses on the topic "Bergman spaces"

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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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Leeuwen, Sweitse Johannes van [Verfasser]. "Invariant Bergman spaces / Sweitse Johannes van Leeuwen." Hannover : Technische Informationsbibliothek und Universitätsbibliothek Hannover (TIB), 2012. http://d-nb.info/1025757777/34.

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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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Zinner, Martin. "Some topics in Bergman spaces with normal weights." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=982571712.

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Sola, Alan. "Conformal Maps, Bergman Spaces, and Random Growth Models." Doctoral thesis, KTH, Matematik (Avd.), 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-12364.

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This thesis consists of an introduction and five research papers on topics related to conformal mapping, the Loewner equation and its applications, and Bergman-type spaces of holomorphic functions. The first two papers are devoted to the study of integral means of derivatives of conformal mappings. In Paper I, we present improved upper estimates of the universal means spectrum of conformal mappingsof the unit disk. These estimates rely on inequalities  obtained by Hedenmalm and Shimorin using Bergman space techniques, and on computer calculations. Paper II is a survey of recent results on the universal means spectrum, with particular emphasis on Bergman spacetechniques.Paper III concerns Bergman-type spaces of holomorphic functions in subsets of $\textbf{C}^d$ and their reproducing kernel functions. By expanding the norm of a function in a Bergman space along the zero variety of a polynomial, we obtain a series expansion of reproducing kernel functions in terms of kernels associated with lower-dimensionalspaces of holomorphic functions. We show how this general approach can be used to explicitly compute kernel functions for certain weighted Bergman and Bargmann-Fock spaces defined in domains in $\textbf{C}^2$.The last two papers contribute to the theory of Loewner chains and theirapplications in the analysis of planar random growth model defined in terms of compositions of conformal maps.In Paper IV, we study Loewner chains generated by unimodular L\'evy processes.We first establish the existence of a capacity scaling limit for the associated growing hulls in terms of whole-plane Loewner chains driven by a time-reversed process. We then analyze the properties of Loewner chains associated with a class of two-parameter compound Poisson processes, and we describe the dependence of the geometric properties of the hulls on the parameters of the driving process. In Paper V, we consider a variation of the Hastings-Levitov growth model, with anisotropic growth. We again establish results concerning scaling limits, when the number of compositions increases and the basic conformal mappings tends to the identity. We show that the resulting limit sets can be associated with solutions to the Loewner equation.We also prove that, in the limit, the evolution of harmonic measure on the boundary is deterministic and is determined by the flow associated with an ordinary differential equation, and we give a description of the fluctuations around this deterministic limit flow.

QC 20100414

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Fleeman, Matthew. "Putnam's Inequality and Analytic Content in the Bergman Space." Scholar Commons, 2016. http://scholarcommons.usf.edu/etd/6238.

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In this dissertation we are interested in studying two extremal problems in the Bergman space. The topics are divided into three chapters. In Chapter 2, we study Putnam’s inequality in the Bergman space setting. In [32], the authors showed that Putnam’s inequality for the norm of self-commutators can be improved by a factor of 1 for Toeplitz operators with analytic symbol φ acting on the Bergman space A2(Ω). This improved upper bound is sharp when φ(Ω) is a disk. We show that disks are the only domains for which the upper bound is attained. In Chapter 3, we consider the problem of finding the best approximation to z ̄ in the Bergman space A2(Ω). We show that this best approximation is the derivative of the solution to the Dirichlet problem on ∂Ω with data |z|2 and give examples of domains where the best approximation is a polynomial, or a rational function. Finally, in Chapter 4 we study Bergman analytic content, which measures the L2(Ω)-distance between z ̄ and the Bergman space A2(Ω). We compute the Bergman analytic content of simply connected quadrature domains with quadrature formula supported at one point, and we also determine the function f ∈ A2(Ω) that best approximates z ̄. We show that, for simply connected domains, the square of Bergman analytic content is equal to torsional rigidity from classical elasticity theory, while for multiply connected domains these two domain constants are not equivalent in general.
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MONTI, MATTEO. "Some aspects of Analysis on symmetric spaces and homogeneous trees: from Radon transform to Bergman spaces." Doctoral thesis, Università degli studi di Genova, 2022. http://hdl.handle.net/11567/1093794.

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The thesis is focused on the Analysis on two classes of non Euclidean spaces: the symmetric spaces of the noncompact type and the homogeneous trees. I first solve in both the settings the problem of the Unitarization of the Radon transform. The last chapter is devoted to the study of the harmonic Bergman spaces on homogeneous trees.
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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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SALOGNI, FRANCESCA. "Harmonic Bergman spaces, Hardy-type spaces and harmonic analysis of a symmetric diffusion semigroup on R^n." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2013. http://hdl.handle.net/10281/41814.

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This thesis is divided into two parts, which deal with quite diverse subjects. The first part is, in turn, divided into two chapters. The first focuses on the development of new function spaces in $R^n$, called generalized Bergman spaces, and on their application to the Hardy space $H^1(R^n)$. The second is devoted to the theory of Bergman spaces on noncompact Riemannian manifolds which possess the doubling property and to its relationships with spaces of Hardy type. The latter are tailored to produce endpoint estimates for interesting operators, mainly related to the Laplace-Beltrami operator. The second part is devoted to the study of some interesting properties of the operator $A f = -1/2 \Delta f- x \cdot \nabla f \forall f \in C_c^\infty (R^n)$, which is essentially self-adjoint with respect to the measure $d \gamma_{-1}(x) = \pi^{n/2} \e^{|x|^2} d \lambda (x) \forall x \in R^n$, where $\lambda$ denotes the Lebesgue measure, and of the semigroup that $A$ generates.
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Books on the topic "Bergman spaces"

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Hedenmalm, Haakan, Boris Korenblum, and Kehe Zhu. Theory of Bergman Spaces. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-0497-8.

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Hedenmalm, Haakan. Theory of Bergman Spaces. New York, NY: Springer New York, 2000.

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Boris, Korenblum, and Zhu Kehe 1961-, eds. Theory of Bergman spaces. New York: Springer, 2000.

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Borichev, Alexander, Håkan Hedenmalm, and Kehe Zhu, eds. Bergman Spaces and Related Topics in Complex Analysis. Providence, Rhode Island: American Mathematical Society, 2006. http://dx.doi.org/10.1090/conm/404.

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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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Jevtić, Miroljub, Dragan Vukotić, and Miloš Arsenović. Taylor Coefficients and Coefficient Multipliers of Hardy and Bergman-Type Spaces. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45644-7.

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

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Boris, Korenblum, Borichev Alexander A. 1963-, Hedenmalm Haakan, and Zhu Kehe 1961-, eds. Bergman spaces and related topics in complex analysis: Proceedings of a conference in honor of Boris Korenblum's 80th birthday, November 20-22, 2003, Barcelona, Spain. Providence, R.I: American Mathematical Society, 2006.

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Guo, Kunyu, and Hansong Huang. Multiplication Operators on the Bergman Space. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-46845-6.

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Holdar, Magdalena. Scenography in action: Space, time and movement in theatre productions by Ingmar Bergman. Stockholm: Konstvetenskapliga institutionen, 2005.

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Book chapters on the topic "Bergman spaces"

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Alpay, Daniel. "Bergman Spaces." In An Advanced Complex Analysis Problem Book, 461–74. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16059-7_10.

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Zhu, Kehe. "Bergman spaces." In Mathematical Surveys and Monographs, 65–100. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/surv/138/04.

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Duren, Peter, and Alexander Schuster. "Overview." In Bergman Spaces, 1–5. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/surv/100/01.

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Duren, Peter, and Alexander Schuster. "The Bergman kernel function." In Bergman Spaces, 7–23. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/surv/100/02.

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Duren, Peter, and Alexander Schuster. "Linear space properties." In Bergman Spaces, 25–72. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/surv/100/03.

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Duren, Peter, and Alexander Schuster. "Analytic properties." In Bergman Spaces, 73–91. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/surv/100/04.

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Duren, Peter, and Alexander Schuster. "Zero-sets." In Bergman Spaces, 93–117. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/surv/100/05.

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Duren, Peter, and Alexander Schuster. "Contractive zero-divisors." In Bergman Spaces, 119–52. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/surv/100/06.

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Duren, Peter, and Alexander Schuster. "Sampling and interpolation." In Bergman Spaces, 153–95. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/surv/100/07.

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Duren, Peter, and Alexander Schuster. "Proofs of sampling and interpolation theorems." In Bergman Spaces, 197–244. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/surv/100/08.

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Conference papers on the topic "Bergman spaces"

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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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"Weissler type inequalities in Bergman spaces." In Уфимская осенняя математическая школа - 2022. Т.1. Baskir State University, 2022. http://dx.doi.org/10.33184/mnkuomsh1t-2022-09-28.37.

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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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Абанин, Александр. "Path components of the set of (weighted) composition operators on Bergman spaces." In International scientific conference "Ufa autumn mathematical school - 2021". Baskir State University, 2021. http://dx.doi.org/10.33184/mnkuomsh1t-2021-10-06.34.

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Jafarzadeh, Bagher. "Some Structural Properties of Weighted Sub‐Bergman Spaces Associated to Finite Blaschke Products." In ICMS INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCE. American Institute of Physics, 2010. http://dx.doi.org/10.1063/1.3525152.

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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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Carmen Reguera, María. "Toeplitz products on the Bergman space." In VI International Course of Mathematical Analysis in Andalusia. WORLD SCIENTIFIC, 2016. http://dx.doi.org/10.1142/9789813147645_0009.

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LUSANNA, LUCA. "SPACE-TIME, GENERAL COVARIANCE, DIRAC-BERGMANN OBSERVABLES AND NON-INERTIAL FRAMES." In Proceedings of the 25th Johns Hopkins Workshop on Current Problems in Particle Theory. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812791368_0005.

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Nandi, Souransu, and Tarunraj Singh. "Hypo/Hyperglycemic Constrained Design of IV Insulin Control for Type 1 Diabetic Patients With Meal and Initial Condition Uncertainties Using Sequential Quadratic Programming." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-87742.

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The focus of this paper is on the development of an open loop controller for type 1 diabetic patients which is robust to meal and initial condition uncertainties in the presence of hypo- and hyperglycemic constraints. Bernstein polynomials are used to parametrize the evolving uncertain blood-glucose. The unique bounding properties of these polynomials are then used to enforce the desired glycemic constraints. A convex optimization problem is posed in the perturbation space of the model and is solved repeatedly to sequentially converge on a sub-optimal solution. The proposed approach is demonstrated on the classic Bergman model for Type 1 diabetic patients.
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