Fourier Meets Hilbert and Riesz: An Introduction to the Corresponding Transforms

René Erlin Castillo

Published by De Gruyter 2023

Fourier Meets Hilbert and Riesz

An Introduction to the Corresponding Transforms

René Erlin Castillo

Volume 87 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783110784091

Overview
Contents

About this book

This book provides an introduction into the modern theory of classical harmonic analysis, dealing with Fourier analysis and the most elementary singular integral operators, the Hilbert transform and Riesz transforms. Ideal for self-study or a one semester course in Fourier analysis, included are detailed examples and exercises.

Explains how ideas from harmonic analysis are used in the analysis of various important singular integral transforms.
Clean and systematic presentation of theorems and proofs.
Ideal for self-study or a course in Fourier analysis.

Author / Editor information

René Erlin Castillo, Nationale U of Colombia, Colombia.

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	VII
Contents Publicly Available Download PDF	IX
1 Fundamental concepts Requires Authentication Unlicensed Licensed Download PDF	1
2 Fourier series Requires Authentication Unlicensed Licensed Download PDF	37
3 Schwartz spaces S(ℝⁿ) Requires Authentication Unlicensed Licensed Download PDF	95
4 Distribution functions Requires Authentication Unlicensed Licensed Download PDF	129
5 Three-fold approach to the Hilbert transform Requires Authentication Unlicensed Licensed Download PDF	171
6 Hilbert transform in L₂(ℝ) Requires Authentication Unlicensed Licensed Download PDF	217
7 Embedding and strong L_p boundedness for the Hilbert transform Requires Authentication Unlicensed Licensed Download PDF	243
8 Riesz transform Requires Authentication Unlicensed Licensed Download PDF	261
Appendix A Requires Authentication Unlicensed Licensed Download PDF	277
Bibliography Requires Authentication Unlicensed Licensed Download PDF	289
Index Requires Authentication Unlicensed Licensed Download PDF	291

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Institutional libraries, researchers and graduate students.
Pages
- Front matter: 10
- Main content: 296
Illustrations
- Illustrations: 11
Keywords: Fourier transform; Hilbert transform; Riesz trransform.

eBook

Published: July 5, 2022
ISBN: 9783110784091

Hardcover

Published: August 1, 2022
ISBN: 9783110784053