Function Theory and $/ell ^p$ Spaces
Seiten
2020
American Mathematical Society (Verlag)
978-1-4704-5593-4 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-5593-4 (ISBN)
The classical $/ell^{p}$ sequence spaces have been a mainstay in Banach spaces. This book reviews some of the foundational results in this area as well as connects them to the function theory of the associated spaces $/ell^{p}_{A}$ of analytic functions whose Taylor coefficients belong to $/ell^p$.
The classical $/ell^{p}$ 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 $/ell^{p}_{A}$ of analytic functions whose Taylor coefficients belong to $/ell^p$. Relations between the Banach space $/ell^p$ 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 $/ell^{p}_{A}$ and a discussion of the Wiener algebra $/ell^{1}_{A}$. 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.
The classical $/ell^{p}$ 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 $/ell^{p}_{A}$ of analytic functions whose Taylor coefficients belong to $/ell^p$. Relations between the Banach space $/ell^p$ 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 $/ell^{p}_{A}$ and a discussion of the Wiener algebra $/ell^{1}_{A}$. 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.
Raymond Cheng,, Old Dominion University, Norfolk, VA Javad Mashreghi, Laval University, Quebec City, QC, Canada William T. Ross University of Richmond, VA
The basics of $/ell^p$; Frames
The geometry of $/ell^p$; Weak parallelogram laws
Hardy and Bergman spaces; $/ell^p$ as a function space
Some operators on $/ell^p_A$; Extremal functions
Zeros of $/ell^p_A$ functions
The shift
The backward shift
Multipliers of $/ell^p_A$; The Wiener algebra
Bibliography
Author index
Subject index.
| Erscheinungsdatum | 03.08.2020 |
|---|---|
| Reihe/Serie | University Lecture Series |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 430 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-4704-5593-5 / 1470455935 |
| ISBN-13 | 978-1-4704-5593-4 / 9781470455934 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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