Classical Fourier Analysis
Seiten
2014
|
3rd ed. 2014
Springer-Verlag New York Inc.
978-1-4939-1193-6 (ISBN)
Springer-Verlag New York Inc.
978-1-4939-1193-6 (ISBN)
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.
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 for the existing exercises, new exercises, and improved references.
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 for the existing exercises, new exercises, and improved references.
Loukas Grafakos is a Professor of Mathematics at the University of Missouri at Columbia.
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.
| Erscheint lt. Verlag | 19.11.2014 |
|---|---|
| Reihe/Serie | Graduate Texts in Mathematics ; 249 |
| Zusatzinfo | 2 Illustrations, color; 12 Illustrations, black and white; XVII, 638 p. 14 illus., 2 illus. in color. |
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Schlagworte | Bessel functions • classical fourier analysis • Fourier-Analysis • Functional Analysis • Gibbs phenomenon • Littlewood-Paley theory • Spherical Fourier inversion • Tauberian theorems |
| ISBN-10 | 1-4939-1193-7 / 1493911937 |
| ISBN-13 | 978-1-4939-1193-6 / 9781493911936 |
| Zustand | Neuware |
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