Mendeley出力
＜図書＞
The Hilbert transform of Schwartz distributions and applications
| 責任表示 | J.N. Pandey |
|---|---|
| シリーズ | Pure and applied mathematics |
| データ種別 | 図書 |
| 出版情報 | New York : John Wiley & Sons , c1996 |
| 本文言語 | 英語 |
| 大きさ | xvi, 262 p. : ill. ; 25 cm |
| 概要 | This book provides a modern and up-to-date treatment of the Hilbert transform of distributions and the space of periodic distributions. Taking a simple and effective approach to a complex subject, thi... volume is a first-rate textbook at the graduate level as well as an extremely useful reference for mathematicians, applied scientists, and engineers. The author, a leading authority in the field, shares with the reader many new results from his exhaustive research on the Hilbert transform of Schwartz distributions. He describes in detail how to use the Hilbert transform to solve theoretical and physical problems in a wide range of disciplines; these include aerofoil problems, dispersion relations, high-energy physics, potential theory problems, and others. Innovative at every step, J. N. Pandey provides a new definition for the Hilbert transform of periodic functions, which is especially useful for those working in the area of signal processing for computational purposes. This definition could also form the basis for a unified theory of the Hilbert transform of periodic, as well as nonperiodic, functions. The Hilbert transform and the approximate Hilbert transform of periodic functions are worked out in detail for the first time in book form and can be used to solve Laplace's equation with periodic boundary conditions. Among the many theoretical results proved in this book is a Paley-Wiener type theorem giving the characterization of functions and generalized functions whose Fourier transforms are supported in certain orthants of Rn. Placing a strong emphasis on easy application of theory and techniques, the book generalizes the Hilbert problem in higher dimensions and solves it in function spaces as well as in generalized function spaces. It simplifies the one-dimensional transform of distributions; provides solutions to the distributional Hilbert problems and singular integral equations; and covers the intrinsic definition of the testing function spaces and its topology. The book includes exercises and review material for all major topics, and incorporates classical and distributional problems into the main text. Thorough and accessible, it explores new ways to use this important integral transform, and reinforces its value in both mathematical research and applied science. The Hilbert transform made accessible with many new formulas and definitions Written by today's foremost expert on the Hilbert transform of generalized functions, this combined text and reference covers the Hilbert transform of distributions and the space of periodic distributions. The author provides a consistently accessible treatment of this advanced-level subject and teaches techniques that can be easily applied to theoretical and physical problems encountered by mathematicians, applied scientists, and graduate students in mathematics and engineering. Introducing many new inversion formulas that have been developed and applied by the author and his research associates, the book: Provides solutions to the distributional Hilbert problem and singular integral equations Focuses on the Hilbert transform of Schwartz distributions, giving intrinsic definitions of the space H(D) and its topology Covers the Paley-Wiener theorem and provides many important theoretical results of importance to research mathematicians Provides the characterization of functions and generalized functions whose Fourier transforms are supported in certain orthants of Rn Offers a new definition of the Hilbert transform of the periodic function that can be used for computational purposes in signal processing Develops the theory of the Hilbert transform of periodic distributions and the approximate Hilbert transform of periodic distributions Provides exercises at the end of each chapter-useful to professors in planning assignments, tests, and problems 続きを見る |
所蔵情報
| 状態 | 巻次 | 所蔵場所 | 請求記号 | 刷年 | 文庫名称 | 資料番号 | コメント | 予約・取寄 | 複写申込 | 自動書庫 |
|---|---|---|---|---|---|---|---|---|---|---|
|
|
: cloth | 理系図3F 数理独自 | PAND/5/1 | 1996 |
|
023211996004215 |
|
書誌詳細
| 別書名 | その他のタイトル:A Wiley-Interscience publication |
|---|---|
| 一般注記 | "A Wiley-Interscience Publication" Includes bibliography (p. 249-253), index and notation index |
| 著者標目 | *Pandey, J. N |
| 件 名 | LCSH:Hilbert transform LCSH:Schwartz distributions |
| 分 類 | LCC:QA432 DC20:515/.782 NDC8:415.5 |
| 書誌ID | 1001400312 |
| ISBN | 0471033731 |
| NCID | BA27183073 |
| 巻冊次 | : cloth ; ISBN:0471033731 |
| 登録日 | 2009.11.02 |
| 更新日 | 2017.10.03 |