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.- Smoothness and Function Spaces.- BMO and Carleson Measures.- Singular Integrals of Nonconvolution Type.- Weighted Inequalities.- Boundedness and Convergence of Fourier Integrals.- Time-Frequency Analysis and the Carleson-Hunt Theorem.- Glossary.- References.- Index.-
- ISBN: 978-0-387-09433-5
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 700
- Fecha Publicación: 01/01/2009
- Nº Volúmenes: 1
- Idioma: Inglés