Fourier Analysis: An Introduction Elias M. Stein and Rami Shakarchi is an English-language textbook aimed at mathematicians and professionals. This first volume provides a clear introduction to Fourier analysis and the core areas of mathematical analysis.
The book covers the basic principles of Fourier analysis, with attention to convergence, summation of Fourier series, and applications such as inequalities and the Radon transform. It then goes on to explain the Fourier transform and its application in partial differential equations. This first volume concludes with Fourier theory for finite abelian groups, including applications in number theory.
Thanks to a balance between conceptual insights and technical foundations, this work is suitable for students and professionals in, among other fields, mathematics, physics, and engineering. The content connects to topics such as functional analysis and transformations.
The book is part of the Princeton Lectures in Analysis and is a valuable reference work that makes clear the connections between different areas of mathematical analysis.