Author: Alexander P. SchusterPublisher:
ISBN:
Category :
Languages : en
Pages : 196
Book Description
Sampling and Interpolation in Bergman Spaces
Author: Alexander P. SchusterPublisher:
ISBN:
Category :
Languages : en
Pages : 196
Book Description
Bergman Spaces
Author: Peter L. DurenPublisher: American Mathematical Soc.
ISBN: 0821808109
Category : Mathematics
Languages : en
Pages : 330
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.
Interpolation and Sampling in Spaces of Analytic Functions
Author: Kristian SeipPublisher: American Mathematical Soc.
ISBN: 0821835548
Category : Mathematics
Languages : en
Pages : 153
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
Regular Sets of Sampling and Interpolation for Weighted Bergman Spaces
Author: Kristian SeipTheory of Bergman Spaces
Author: Hakan HedenmalmPublisher: Springer Science & Business Media
ISBN: 1461204976
Category : Mathematics
Languages : en
Pages : 299
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.
Interpolation and Sampling in Analytic Tent Spaces
Author: Caleb ParksPublisher:
ISBN:
Category :
Languages : en
Pages : 154
Book Description
Introduced by Coifman, Meyer, and Stein, the tent spaces have seen wide applications in harmonic analysis. Their analytic cousins have seen some applications involving the derivatives of Hardy space functions. Moreover, the tent spaces have been a recent focus of research. We introduce the concept of interpolating and sampling sequences for analytic tent spaces analogously to the same concepts for Bergman spaces. We then characterize such sequences in terms of Seip's upper and lower uniform density. We accomplish this by exploiting a kind of Mobius invariance for the tent spaces.
Bergman Spaces
Author: Peter DurenPublisher: American Mathematical Society
ISBN: 082184315X
Category : Mathematics
Languages : en
Pages : 330
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.
Weighted Bergman Spaces Induced by Rapidly Increasing Weights
Author: Jose Angel PelaezPublisher: American Mathematical Soc.
ISBN: 0821888021
Category : Mathematics
Languages : en
Pages : 136
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 $A^p_\omega$.
Functions with Disconnected Spectrum
Author: Alexander M. OlevskiiPublisher: American Mathematical Soc.
ISBN: 147042889X
Category : Mathematics
Languages : en
Pages : 152
Book Description
The classical sampling problem is to reconstruct entire functions with given spectrum S from their values on a discrete set L. From the geometric point of view, the possibility of such reconstruction is equivalent to determining for which sets L the exponential system with frequencies in L forms a frame in the space L2(S). The book also treats the problem of interpolation of discrete functions by analytic ones with spectrum in S and the problem of completeness of discrete translates. The size and arithmetic structure of both the spectrum S and the discrete set L play a crucial role in these problems. After an elementary introduction, the authors give a new presentation of classical results due to Beurling, Kahane, and Landau. The main part of the book focuses on recent progress in the area, such as construction of universal sampling sets, high-dimensional and non-analytic phenomena. The reader will see how methods of harmonic and complex analysis interplay with various important concepts in different areas, such as Minkowski's lattice, Kolmogorov's width, and Meyer's quasicrystals. The book is addressed to graduate students and researchers interested in analysis and its applications. Due to its many exercises, mostly given with hints, the book could be useful for undergraduates.
Extended Abstracts Fall 2019
Author: Evgeny AbakumovPublisher: Springer Nature
ISBN: 3030744175
Category : Mathematics
Languages : en
Pages : 223
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.