<電子ブック>
A Basis Theory Primer : Expanded Edition / by Christopher Heil
(Applied and Numerical Harmonic Analysis. ISSN:22965017)
版 | 1st ed. 2011. |
---|---|
出版者 | Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser |
出版年 | 2011 |
本文言語 | 英語 |
大きさ | XXV, 537 p. 42 illus : online resource |
著者標目 | *Heil, Christopher author SpringerLink (Online service) |
件 名 | LCSH:Harmonic analysis LCSH:Engineering mathematics LCSH:Engineering -- Data processing 全ての件名で検索 LCSH:Functional analysis LCSH:Fourier analysis LCSH:Mathematics LCSH:Signal processing FREE:Abstract Harmonic Analysis FREE:Mathematical and Computational Engineering Applications FREE:Functional Analysis FREE:Fourier Analysis FREE:Applications of Mathematics FREE:Signal, Speech and Image Processing |
一般注記 | ANHA Series Preface -- Preface -- General Notation -- Part I. A Primer on Functional Analysis -- Banach Spaces and Operator Theory -- Functional Analysis -- Part II. Bases and Frames -- Unconditional Convergence of Series in Banach and Hilbert Spaces -- Bases in Banach Spaces -- Biorthogonality, Minimality, and More About Bases -- Unconditional Bases in Banach Spaces -- Bessel Sequences and Bases in Hilbert Spaces -- Frames in Hilbert Spaces -- Part III. Bases and Frames in Applied Harmonic Analysis -- The Fourier Transform on the Real Line -- Sampling, Weighted Exponentials, and Translations -- Gabor Bases and Frames -- Wavelet Bases and Frames -- Part IV. Fourier Series -- Fourier Series -- Basic Properties of Fourier Series -- Part V. Appendices -- Lebesgue Measure and Integration -- Compact and Hilbert–Schmidt Operators -- Hints for Exercises -- Index of Symbols -- References -- Index The classical subject of bases in Banach spaces has taken on a new life in the modern development of applied harmonic analysis. This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and its use in both applied and classical harmonic analysis. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory. * Part I develops the functional analysis that underlies most of the concepts presented in the later parts of the text. * Part II presents the abstract theory of bases and frames in Banach and Hilbert spaces, including the classical topics of convergence, Schauder bases, biorthogonal systems, and unconditional bases, followed by the more recent topics of Riesz bases and frames in Hilbert spaces. * Part III relates bases and frames to applied harmonic analysis, including sampling theory, Gabor analysis, and wavelet theory. * Part IV deals with classical harmonic analysis and Fourier series, emphasizing the role played by bases, which is a different viewpoint from that taken in most discussions of Fourier series. Key features: * Self-contained presentation with clear proofs accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications. * Extensive exercises complement the text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses; hints for selected exercises are included at the end of the book. * A separate solutions manual is available for instructors upon request at: www.birkhauser-science.com/978-0-8176-4686-8/. * No other text develops the ties between classical basis theory and its modern uses in applied harmonic analysis. A Basis Theory Primer is suitable for independent study or as the basis for a graduate-level course. Instructors have several options for building a course around the text depending on the level and background of their students HTTP:URL=https://doi.org/10.1007/978-0-8176-4687-5 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
|
Springer eBooks | 9780817646875 |
|
電子リソース |
|
EB00238568 |
書誌詳細を非表示
データ種別 | 電子ブック |
---|---|
分 類 | LCC:QA403-403.3 DC23:515.785 |
書誌ID | 4000115145 |
ISBN | 9780817646875 |
類似資料
この資料の利用統計
このページへのアクセス回数:3回
※2017年9月4日以降