Fourier meets Hilbert and Riesz : an introduction to the corresponding transforms / René Erlin Castillo.

Format:

Book

Author/Creator:

Castillo, René Erlin, author.

Series:

De Gruyter studies in mathematics ; Volume 87.

De Gruyter Studies in Mathematics, 0179-0986 ; Volume 87

Language:

English

Subjects (All):

Transformations (Mathematics).

Genre:

Textbooks.

Physical Description:

1 online resource (306 pages) : illustrations

Place of Publication:

Berlin ; Boston : Walter de Gruyter GmbH, [2022]

Summary:

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Contents:

Frontmatter

Preface

Contents

1 Fundamental concepts

2 Fourier series

3 Schwartz spaces S(ℝn)

4 Distribution functions

5 Three-fold approach to the Hilbert transform

6 Hilbert transform in L2(ℝ)

7 Embedding and strong Lp boundedness for the Hilbert transform

8 Riesz transform

Appendix A

Bibliography

Index

Notes:

This book is based on lecture notes from a special topics course on advanced analysis offered at Universidad Nacional de Columbia during the spring semester of 2019"--Preface.

Includes bibliographical references and index.

Description based on print version record.

Current Copyright Fee: GBP22.50 0.

ISBN:

9783110784091

9783110784121

3-11-078409-2

OCLC:

1334344273