Theory of Bergman Spaces

Theory of Bergman Spaces
Author :
Publisher : Springer Science & Business Media
Total Pages : 299
Release :
ISBN-10 : 9781461204978
ISBN-13 : 1461204976
Rating : 4/5 (78 Downloads)

Synopsis Theory of Bergman Spaces by : Hakan Hedenmalm

Fifteen years ago, most mathematicians who worked in the intersection of function theory and operator theory thought that progress on the Bergman spaces was unlikely, yet today the situation has completely changed. For several years, research interest and activity have expanded in this area and there are now rich theories describing the Bergman spaces and their operators. This book is a timely treatment of the theory, written by three of the major players in the field.

Theory of Bergman Spaces

Theory of Bergman Spaces
Author :
Publisher : Springer Science & Business Media
Total Pages : 304
Release :
ISBN-10 : 9780387987910
ISBN-13 : 0387987916
Rating : 4/5 (10 Downloads)

Synopsis Theory of Bergman Spaces by : Hakan Hedenmalm

Fifteen years ago, most mathematicians who worked in the intersection of function theory and operator theory thought that progress on the Bergman spaces was unlikely, yet today the situation has completely changed. For several years, research interest and activity have expanded in this area and there are now rich theories describing the Bergman spaces and their operators. This book is a timely treatment of the theory, written by three of the major players in the field.

Theory of Bergman Spaces

Theory of Bergman Spaces
Author :
Publisher : Springer
Total Pages : 0
Release :
ISBN-10 : 1461267897
ISBN-13 : 9781461267898
Rating : 4/5 (97 Downloads)

Synopsis Theory of Bergman Spaces by : Hakan Hedenmalm

Fifteen years ago, most mathematicians who worked in the intersection of function theory and operator theory thought that progress on the Bergman spaces was unlikely, yet today the situation has completely changed. For several years, research interest and activity have expanded in this area and there are now rich theories describing the Bergman spaces and their operators. This book is a timely treatment of the theory, written by three of the major players in the field.

Bergman Spaces

Bergman Spaces
Author :
Publisher : American Mathematical Society
Total Pages : 330
Release :
ISBN-10 : 9780821843154
ISBN-13 : 082184315X
Rating : 4/5 (54 Downloads)

Synopsis Bergman Spaces by : Peter Duren

The modern subject of Bergman spaces is a masterful blend of complex function theory with functional analysis and operator theory. It has much in common with Hardy spaces but involves new elements such as hyperbolic geometry, reproducing kernels, and biharmonic Green functions. This book develops background material and provides a self-contained introduction to a broad range of old and new topics in Bergman spaces, including recent advances on interpolation and sampling, contractive zero-divisors, and invariant subspaces. It is accessible to anyone who has studied basic real and complex analysis at the graduate level.

Operator Theory in Function Spaces

Operator Theory in Function Spaces
Author :
Publisher : American Mathematical Soc.
Total Pages : 368
Release :
ISBN-10 : 9780821839652
ISBN-13 : 0821839659
Rating : 4/5 (52 Downloads)

Synopsis Operator Theory in Function Spaces by : Kehe Zhu

This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes. Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study. The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.

Weighted Bergman Spaces Induced by Rapidly Increasing Weights

Weighted Bergman Spaces Induced by Rapidly Increasing Weights
Author :
Publisher : American Mathematical Soc.
Total Pages : 136
Release :
ISBN-10 : 9780821888025
ISBN-13 : 0821888021
Rating : 4/5 (25 Downloads)

Synopsis Weighted Bergman Spaces Induced by Rapidly Increasing Weights by : Jose Angel Pelaez

This monograph is devoted to the study of the weighted Bergman space $A^p_\omega$ of the unit disc $\mathbb{D}$ that is induced by a radial continuous weight $\omega$ satisfying $\lim_{r\to 1^-}\frac{\int_r^1\omega(s)\,ds}{\omega(r)(1-r)}=\infty.$ Every such $A^p_\omega$ lies between the Hardy space $H^p$ and every classical weighted Bergman space $A^p_\alpha$. Even if it is well known that $H^p$ is the limit of $A^p_\alpha$, as $\alpha\to-1$, in many respects, it is shown that $A^p_\omega$ lies ``closer'' to $H^p$ than any $A^p_\alpha$, and that several finer function-theoretic properties of $A^p_\alpha$ do not carry over to $A^p_\omega$.

Function Theory and ℓp Spaces

Function Theory and ℓp Spaces
Author :
Publisher : American Mathematical Soc.
Total Pages : 219
Release :
ISBN-10 : 9781470455934
ISBN-13 : 1470455935
Rating : 4/5 (34 Downloads)

Synopsis Function Theory and ℓp Spaces by : Raymond Cheng

The classical ℓp sequence spaces have been a mainstay in Banach spaces. This book reviews some of the foundational results in this area (the basic inequalities, duality, convexity, geometry) as well as connects them to the function theory (boundary growth conditions, zero sets, extremal functions, multipliers, operator theory) of the associated spaces ℓpA of analytic functions whose Taylor coefficients belong to ℓp. Relations between the Banach space ℓp and its associated function space are uncovered using tools from Banach space geometry, including Birkhoff-James orthogonality and the resulting Pythagorean inequalities. The authors survey the literature on all of this material, including a discussion of the multipliers of ℓpA and a discussion of the Wiener algebra ℓ1A. Except for some basic measure theory, functional analysis, and complex analysis, which the reader is expected to know, the material in this book is self-contained and detailed proofs of nearly all the results are given. Each chapter concludes with some end notes that give proper references, historical background, and avenues for further exploration.

Holomorphic Spaces

Holomorphic Spaces
Author :
Publisher : Cambridge University Press
Total Pages : 490
Release :
ISBN-10 : 0521631939
ISBN-13 : 9780521631938
Rating : 4/5 (39 Downloads)

Synopsis Holomorphic Spaces by : Sheldon Jay Axler

Expository articles describing the role Hardy spaces, Bergman spaces, Dirichlet spaces, and Hankel and Toeplitz operators play in modern analysis.

Noncommutative Function-Theoretic Operator Theory and Applications

Noncommutative Function-Theoretic Operator Theory and Applications
Author :
Publisher : Cambridge University Press
Total Pages : 440
Release :
ISBN-10 : 9781009020107
ISBN-13 : 1009020102
Rating : 4/5 (07 Downloads)

Synopsis Noncommutative Function-Theoretic Operator Theory and Applications by : Joseph A. Ball

This concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system theory ideas and reproducing kernel techniques, the book then covers representations of backward-shift-invariant subspaces in the Hardy space as ranges of observability operators, and representations for forward-shift-invariant subspaces via a Beurling–Lax representer equal to the transfer function of the linear system. This pair of backward-shift-invariant and forward-shift-invariant subspace form a generalized orthogonal decomposition of the ambient Hardy space. All this leads to the de Branges–Rovnyak model theory and characteristic operator function for a Hilbert space contraction operator. The chapters that follow generalize the system theory and reproducing kernel techniques to enable an extension of the ideas above to weighted Bergman space multivariable settings.

Quadrature Domains and Their Applications

Quadrature Domains and Their Applications
Author :
Publisher : Springer Science & Business Media
Total Pages : 298
Release :
ISBN-10 : 9783764373160
ISBN-13 : 3764373164
Rating : 4/5 (60 Downloads)

Synopsis Quadrature Domains and Their Applications by : Peter Ebenfelt

Quadrature domains were singled out about 30 years ago by D. Aharonov and H.S. Shapiro in connection with an extremal problem in function theory. Since then, a series of coincidental discoveries put this class of planar domains at the center of crossroads of several quite independent mathematical theories, e.g., potential theory, Riemann surfaces, inverse problems, holomorphic partial differential equations, fluid mechanics, operator theory. The volume is devoted to recent advances in the theory of quadrature domains, illustrating well the multi-facet aspects of their nature. The book contains a large collection of open problems pertaining to the general theme of quadrature domains.