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

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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(s): René Erlin Castillo
Series: De Gruyter Studies in Mathematics, 87
Edition: 1
Publisher: De Gruyter
Year: 2022

Language: English
Pages: 296
City: Berlin
Tags: Fourier Series, Hilbert Transform, Riesz Transform

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