Introduction to Fourier Analysis

Author: Eli M. Stein, Rami Shakarchi
Publisher:
Publish Date: 2006-01-01
Features: As a master in the field of mathematics, the author presents the various aspects of Fourier Transform in an accessible language to readers. Most relevant books in China are either obscure or require substantial prior knowledge, or have a limited scope. This book effectively addresses these issues and is well-coordinated with subsequent topics like Complex Analysis and Real Analysis, offering significant benefits. The book is divided into three parts:
Part 1 introduces the basic theory of Fourier series and its applications in isoperimetric inequalities and uniform distribution.
Part 2 studies Fourier Transform and its applications in classical partial differential equations and Radon Transform.
Part 3 explores Fourier analysis on finite Abelian groups.
Each chapter includes exercises and thought-provoking problems.