The primary goal of this text is to present the theoretical foundation of thefield of Fourier analysis. The only prerequisite for understanding the text is satisfactory completion of a course in measure theory, Lebesgue integration,and complex variables. This book is intended to present the selected topics in some depth and stimulate further study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentalsof analysis on the torus. This material is included for historical reasons, as the genesis of Fourier analysis can be found in trigonometric expansions of periodic functions in several variables. While the 1st edition was published as a single volume, the new edition will contain 120 pp of new material, with an additional chaper on time-frequency analysis and other modern topics. As a result, the book is now being published in 2 separate volumes, containing the modern topics (weighted inequalities, wavelets, atomic decomposition, etc...). Historical notes at the end of each chapter Numerous exercises for each chapter User-friendly exposition with examples illustrating the definitions and ideas INDICE: Preface.- Lp Spaces and Interpolation.- Maximal Functions, FourierTransform, and Distributions.- Fourier Analysis on the Torus.- Singular Integrals of Convolution Type.- Littlewood-Paley Theory and Multipliers.- Gamma andBeta Functions.- Bessel Functions.- Rademacher Functions.- Spherical Coordinates.- Some Trigonometric Identities and Inequalities.- Summation by Parts.- Basic Functional Analysis.- The Minimax Lemma.- The Schur Lemma.- The Whitney Decomposition of Open Sets in Rn.- Smoothness and Vanishing Moments.- Glossary.-References.- Index.
- ISBN: 978-0-387-09431-1
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 505
- Fecha Publicación: 01/09/2008
- Nº Volúmenes: 1
- Idioma: Inglés