Harmonic Analysis on the Real Line - Elijah Liflyand

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Résumé :
This book sketches a path for newcomers into the theory of harmonic analysis on the real line. It presents a collection of both basic, well-known and some less known results that may serve as a background for future research around this topic. Many of these results are also a necessary basis for multivariate extensions. An extensive bibliography, as well as hints to open problems are included. The book can be used as a skeleton for designing certain special courses, but it is also suitable for self-study.

Biographie:
Elijah Liflyand has recently retired from his position at the Department of Mathematics at Bar-Ilan University in Israel, but not from mathematics. He also holds a position at the at the Regional Mathematical Center of Southern Federal University in Rostov-on-Don, Russia. His areas of expertise are in Fourier Analysis, Complex Analysis, and Approximation Theory, among others. With Birkh?user/Springer, he has published two books: Decay of the Fourier Transform (with Alex Iosevich, 2014), and Functions of Bounded Variation and Their Fourier Transforms (in the Applied Numerical and Harmonic Analysis series, 2019)....

Sommaire:
- Introduction. - Classes of Functions. - Fourier Series. - Fourier Transform. - Hilbert Transform. - Hardy Spaces and their Subspaces. - Hardy Inequalities. - Certain Applications.