ENGLISH

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

By Rene Erlin Castillo

Book information

Publisher
de Gruyter
Year
2022
ISBN
9783110784053, 9783110784091, 9783110784121, 2022934767
Language
english
Format
PDF
Filesize
4 MB (4401711 bytes)
Series
De Gruyter Studies in Mathematics, 87
Edition
1
Pages
296\307
Time added
2022-07-13 09:47:04
Fourier seriesHilbert TransformRiesz Transform

Description

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. 1 Fundamental concepts 1 2 Fourier series 37 3 Schwartz spaces S(ℝn) 95 4 Distribution functions 129 5 Three-fold approach to the Hilbert transform 171 6 Hilbert transform in L2(ℝ) 217 7 Embedding and strong Lp boundedness for the Hilbert transform 243 8 Riesz transform 261

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