<電子ブック>
Fourier Analysis on Finite Abelian Groups / by Bao Luong
(Applied and Numerical Harmonic Analysis. ISSN:22965017)
版 | 1st ed. 2009. |
---|---|
出版者 | (Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser) |
出版年 | 2009 |
本文言語 | 英語 |
大きさ | XVI, 159 p : online resource |
著者標目 | *Luong, Bao author SpringerLink (Online service) |
件 名 | LCSH:Mathematical analysis LCSH:Algebra LCSH:Fourier analysis LCSH:Group theory FREE:Analysis FREE:Algebra FREE:Fourier Analysis FREE:Group Theory and Generalizations |
一般注記 | Preface -- Overview -- Chapter 1: Foundation Material -- Results from Group Theory -- Quadratic Congruences -- Chebyshev Systems of Functions -- Chapter 2: The Fourier Transform -- A Special Class of Linear Operators -- Characters -- The Orthogonal Relations for Characters -- The Fourier Transform -- The Fourier Transform of Periodic Functions -- The Inverse Fourier Transform -- The Inversion Formula -- Matrices of the Fourier Transform -- Iterated Fourier Transform -- Is the Fourier Transform a Self-Adjoint Operator? -- The Convolutions Operator -- Banach Algebra -- The Uncertainty Principle -- The Tensor Decomposition -- The Tensor Decomposition of Vector Spaces -- The Fourier Transform and Isometries -- Reduction to Finite Cyclic Groups -- Symmetric and Antisymmetric Functions -- Eigenvalues and Eigenvectors -- Spectrak Theorem -- Ergodic Theorem -- Multiplicities of Eigenvalues -- The Quantum Fourier Transform -- Chapter 3: Quadratic Sums -- 1. The Number G_n(1) -- Reduction Formulas Fourier analysis has been the inspiration for a technological wave of advances in fields such as imaging processing, financial modeling, cryptography, algorithms, and sequence design. This self-contained book provides a thorough look at the Fourier transform, one of the most useful tools in applied mathematics. With countless examples and unique exercise sets at the end of most sections, Fourier Analysis on Finite Abelian Groups is a perfect companion for a first course in Fourier analysis. The first two chapters provide fundamental material for a strong foundation to deal with subsequent chapters. Special topics covered include: * Computing eigenvalues of the Fourier transform * Applications to Banach algebras * Tensor decompositions of the Fourier transform * Quadratic Gaussian sums This book provides a useful introduction for well-prepared undergraduate and graduate students and powerful applications that may appeal to researchers and mathematicians. The only prerequisites are courses in group theory and linear algebra HTTP:URL=https://doi.org/10.1007/978-0-8176-4916-6 |
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 | 9780817649166 |
|
電子リソース |
|
EB00226816 |
書誌詳細を非表示
データ種別 | 電子ブック |
---|---|
分 類 | LCC:QA299.6-433 DC23:515 |
書誌ID | 4000117376 |
ISBN | 9780817649166 |
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:5回
※2017年9月4日以降