Harmonic Analysis on the Real Line: A Path in the Theory

ISBN-13: 9783030818944 / Angielski / Miękka / 2022

Elijah Liflyand

Opis

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.

Recenzje

"This book is very accurately described by its subtitle 'a path in the theory'. The book is at times a textbook, an introduction to harmonic analysis, an essay, or a survey, or some combination of these. ... Some theorems are stated and proved, some are discussed, and others are quickly mentioned. It's not a standard path, but an engaging one, offering insights and connections that are new or not well known." ( Charles N. Moore, Mathematical Reviews, September, 2022)

Spis treści

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

O autorze

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 Birkhäuser/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).