Sampling and Interpolation in Bergman Spaces PDF Download
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Author: Alexander P. Schuster
Publisher:
ISBN:
Category :
Languages : en
Pages : 196
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Book Description
Author: Alexander P. Schuster
Publisher:
ISBN:
Category :
Languages : en
Pages : 196
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Book Description
Author: Kristian Seip
Publisher: American Mathematical Soc.
ISBN: 0821835548
Category : Mathematics
Languages : en
Pages : 153
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Book Description
Based on a series of six lectures given by the author at the University of Michigan, this book is intended as an introduction to the topic of interpolation and sampling in analytic function spaces. The three major topics covered are Nevanlinna-Pick interpolation, Carleson's interpolation theorem, an
Author: Peter L. Duren
Publisher: American Mathematical Soc.
ISBN: 0821808109
Category : Mathematics
Languages : en
Pages : 330
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Book Description
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.
Author: Hakan Hedenmalm
Publisher: Springer Science & Business Media
ISBN: 1461204976
Category : Mathematics
Languages : en
Pages : 299
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Book Description
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.
Author: Peter Duren
Publisher: American Mathematical Society
ISBN: 082184315X
Category : Mathematics
Languages : en
Pages : 330
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Book Description
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.
Author: Peter Ebenfelt
Publisher: Springer Science & Business Media
ISBN: 3764373164
Category : Mathematics
Languages : en
Pages : 298
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Book Description
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.
Author: Jim Agler
Publisher: American Mathematical Society
ISBN: 1470468557
Category : Mathematics
Languages : en
Pages : 330
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Book Description
The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $H^infty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $H^infty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces. The authors then consider the interpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem, and the hereditary functional calculus.
Author: Jose Angel Pelaez
Publisher: American Mathematical Soc.
ISBN: 0821888021
Category : Mathematics
Languages : en
Pages : 136
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Book Description
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 $A^p_\omega$.
Author: Kehe Zhu
Publisher: Springer Science & Business Media
ISBN: 1441988017
Category : Mathematics
Languages : en
Pages : 350
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Book Description
Several natural Lp spaces of analytic functions have been widely studied in the past few decades, including Hardy spaces, Bergman spaces, and Fock spaces. The terms “Hardy spaces” and “Bergman spaces” are by now standard and well established. But the term “Fock spaces” is a different story. Numerous excellent books now exist on the subject of Hardy spaces. Several books about Bergman spaces, including some of the author’s, have also appeared in the past few decades. But there has been no book on the market concerning the Fock spaces. The purpose of this book is to fill that void, especially when many results in the subject are complete by now. This book presents important results and techniques summarized in one place, so that new comers, especially graduate students, have a convenient reference to the subject. This book contains proofs that are new and simpler than the existing ones in the literature. In particular, the book avoids the use of the Heisenberg group, the Fourier transform, and the heat equation. This helps to keep the prerequisites to a minimum. A standard graduate course in each of real analysis, complex analysis, and functional analysis should be sufficient preparation for the reader.
Author: Evgeny Abakumov
Publisher: Springer Nature
ISBN: 3030744175
Category : Mathematics
Languages : en
Pages : 223
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Book Description
This book collects the abstracts of the mini-courses and lectures given during the Intensive Research Program “Spaces of Analytic Functions: Approximation, Interpolation, Sampling” which was held at the Centre de Recerca Matemàtica (Barcelona) in October–December, 2019. The topics covered in this volume are approximation, interpolation and sampling problems in spaces of analytic functions, their applications to spectral theory, Gabor analysis and random analytic functions. In many places in the book, we see how a problem related to one of the topics is tackled with techniques and ideas coming from another. The book will be of interest for specialists in Complex Analysis, Function and Operator theory, Approximation theory, and their applications, but also for young people starting their research in these areas.
