Fourier Analysis on Local Fields
Seiten
2015
Princeton University Press (Verlag)
978-0-691-61812-8 (ISBN)
Princeton University Press (Verlag)
978-0-691-61812-8 (ISBN)
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This book presents a development of the basic facts about harmonic analysis on local fields and the n-dimensional vector spaces over these fields. It focuses almost exclusively on the analogy between the local field and Euclidean cases, with respect to the form of statements, the manner of proof, and the variety of applications. The force of the a
This book presents a development of the basic facts about harmonic analysis on local fields and the n-dimensional vector spaces over these fields. It focuses almost exclusively on the analogy between the local field and Euclidean cases, with respect to the form of statements, the manner of proof, and the variety of applications. The force of the analogy between the local field and Euclidean cases rests in the relationship of the field structures that underlie the respective cases. A complete classification of locally compact, non-discrete fields gives us two examples of connected fields (real and complex numbers); the rest are local fields (p-adic numbers, p-series fields, and their algebraic extensions). The local fields are studied in an effort to extend knowledge of the reals and complexes as locally compact fields. The author's central aim has been to present the basic facts of Fourier analysis on local fields in an accessible form and in the same spirit as in Zygmund's Trigonometric Series (Cambridge, 1968) and in Introduction to Fourier Analysis on Euclidean Spaces by Stein and Weiss (1971). Originally published in 1975.
The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
This book presents a development of the basic facts about harmonic analysis on local fields and the n-dimensional vector spaces over these fields. It focuses almost exclusively on the analogy between the local field and Euclidean cases, with respect to the form of statements, the manner of proof, and the variety of applications. The force of the analogy between the local field and Euclidean cases rests in the relationship of the field structures that underlie the respective cases. A complete classification of locally compact, non-discrete fields gives us two examples of connected fields (real and complex numbers); the rest are local fields (p-adic numbers, p-series fields, and their algebraic extensions). The local fields are studied in an effort to extend knowledge of the reals and complexes as locally compact fields. The author's central aim has been to present the basic facts of Fourier analysis on local fields in an accessible form and in the same spirit as in Zygmund's Trigonometric Series (Cambridge, 1968) and in Introduction to Fourier Analysis on Euclidean Spaces by Stein and Weiss (1971). Originally published in 1975.
The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
*Frontmatter, pg. i*Preface, pg. v*Introduction, pg. vii*Table of Contents, pg. xi*Chapter I: Introduction to local fields, pg. 1*Chapter II: Fourier analysis on K, the one-dimension case, pg. 20*Chapter III. Fourier analysis on Kn., pg. 115*Chapter IV. Regularization and the theory of regular and sub-regular functions, pg. 168*Chapter V. The Littlewood-Paley function and some applications, pg. 195*Chapter VI. Multipliers and singular integral operators, pg. 217*Chapter VII. Conjugate systems of regular functions and an F. and M. Riesz theorem, pg. 241*Chapter VIII. Almost everywhere convergence of Fourier series, pg. 262*Bibliography, pg. 286
| Erscheint lt. Verlag | 8.3.2015 |
|---|---|
| Reihe/Serie | Mathematical Notes |
| Verlagsort | New Jersey |
| Sprache | englisch |
| Maße | 152 x 235 mm |
| Gewicht | 425 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| ISBN-10 | 0-691-61812-7 / 0691618127 |
| ISBN-13 | 978-0-691-61812-8 / 9780691618128 |
| Zustand | Neuware |
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