Harmonic Analysis on the Real Line

A Path in the Theory
1. Auflage 2021
ISBN: 978-3-030-81894-4
Verlag: Springer International Publishing

Buch, Englisch, 197 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 324 g

Reihe: Pathways in Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Liflyand, Elijah

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis

Inhaltsverzeichnis

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

Über Autor(innen)

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).