Exploring Classical Fourier Analysis

Exploring Classical Fourier Analysis is a textbook that covers the fundamental principles of classical Fourier analysis. The book is written in a clear and concise style, and it is designed to be accessible to students with a variety of backgrounds.

The book begins with an overview of the field of Fourier analysis and its importance in mathematics and other fields. It then discusses the basic principles of Fourier series and Fourier transforms.

The book then applies these principles to a variety of specific Fourier analysis problems, such as:

The heat equation
The wave equation
Laplace’s equation
The Schrödinger equation

The book also includes a number of chapters on more advanced topics, such as:

Bessel functions
Gibbs phenomenon
Littlewood-Paley theory
Spherical Fourier inversion
Tauberian theorems
Functional analysis