[PDF] Interpolation And Sampling On The Fock Space eBook

Author : Kehe Zhu
Publisher : Springer Science & Business Media
Page : 350 pages
File Size : 45,72 MB
Release : 2012-05-26
Category : Mathematics
ISBN : 1441988017

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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 : Kristian Seip
Publisher : American Mathematical Soc.
Page : 153 pages
File Size : 34,1 MB
Release : 2004
Category : Mathematics
ISBN : 0821835548

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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 : Kristian Seip
Publisher : American Mathematical Soc.
Page : 156 pages
File Size : 50,50 MB
Release :
Category : Mathematics
ISBN : 9780821882900

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"The book is essentially self-contained. There is an underlying assumption that the reader has a basic knowledge of complex and functional analysis. Beyond that, the reader should have some familiarity with the basic of H[superscript p] theory and BMO."--BOOK JACKET.

Author : Alexander M. Olevskii
Publisher : American Mathematical Soc.
Page : 152 pages
File Size : 29,24 MB
Release : 2016-06-13
Category : Mathematics
ISBN : 147042889X

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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.

Author : Lawrence Zalcman
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 42,59 MB
Release : 2016-05-19
Category : Mathematics
ISBN : 1470417030

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This volume contains the proceedings of the Sixth International Conference on Complex Analysis and Dynamical Systems, held from May 19–24, 2013, in Nahariya, Israel, in honor of David Shoikhet's sixtieth birthday. The papers range over a wide variety of topics in complex analysis, quasiconformal mappings, and complex dynamics. Taken together, the articles provide the reader with a panorama of activity in these areas, drawn by a number of leading figures in the field. They testify to the continued vitality of the interplay between classical and modern analysis. The companion volume (Contemporary Mathematics, Volume 653) is devoted to partial differential equations, differential geometry, and radon transforms.

Author : Kehe Zhu
Publisher : CRC Press
Page : 228 pages
File Size : 24,28 MB
Release : 2019-05-10
Category : Mathematics
ISBN : 1351045539

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This handbook concerns the subject of holomorphic function spaces and operators acting on them. Topics include Bergman spaces, Hardy spaces, Besov/Sobolev spaces, Fock spaces, and the space of Dirichlet series. Operators discussed in the book include Toeplitz operators, Hankel operators, composition operators, and Cowen-Douglas class operators