<電子ブック>
Classical Fourier Analysis / by Loukas Grafakos
(Graduate Texts in Mathematics. ISSN:21975612 ; 249)
版 | 3rd ed. 2014. |
---|---|
出版者 | New York, NY : Springer New York : Imprint: Springer |
出版年 | 2014 |
本文言語 | 英語 |
大きさ | XVII, 638 p. 14 illus., 2 illus. in color : online resource |
著者標目 | *Grafakos, Loukas author SpringerLink (Online service) |
件 名 | LCSH:Fourier analysis LCSH:Harmonic analysis LCSH:Functional analysis FREE:Fourier Analysis FREE:Abstract Harmonic Analysis FREE:Functional Analysis |
一般注記 | Preface -- 1. Lp Spaces and Interpolation -- 2. Maximal Functions, Fourier Transform, and Distributions -- 3. Fourier Series -- 4. Topics on Fourier Series -- 5. Singular Integrals of Convolution Type -- 6. Littlewood–Paley Theory and Multipliers -- 7. Weighted Inequalities -- A. Gamma and Beta Functions -- B. Bessel Functions -- C. Rademacher Functions -- D. Spherical Coordinates -- E. Some Trigonometric Identities and Inequalities -- F. Summation by Parts -- G. Basic Functional Analysis -- H. The Minimax Lemma -- I. Taylor's and Mean Value Theorem in Several Variables -- J. The Whitney Decomposition of Open Sets in Rn -- Glossary -- References -- Index The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition. Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints forthe existing exercises, new exercises, and improved references. Reviews from the Second Edition: “The books cover a large amount of mathematics. They are certainly a valuable and useful addition to the existing literature and can serve as textbooks or as reference books. Students will especially appreciate the extensive collection of exercises.” —Andreas Seager, Mathematical Reviews “This book is very interesting and useful. It is not only a good textbook, but also an indispensable and valuable reference for researchers who are working on analysis and partial differential equations. The readers will certainly benefit a lot from the detailed proofs and the numerous exercises.” —Yang Dachun, zbMATH HTTP:URL=https://doi.org/10.1007/978-1-4939-1194-3 |
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 | 9781493911943 |
|
電子リソース |
|
EB00238039 |
書誌詳細を非表示
データ種別 | 電子ブック |
---|---|
分 類 | LCC:QA403.5-404.5 DC23:5,152,433 |
書誌ID | 4000119358 |
ISBN | 9781493911943 |
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:6回
※2017年9月4日以降