A Guide to Distribution Theory and Fourier Transforms.

TLDR

The book is situated in applied analysis and mathematical physics. The book aims to concisely present the theory of distributions and Fourier transforms, their application to PDEs, and recent topics such as pseudo‑differential operators, wave front sets, wavelets, and quasicrystals. It offers concise exposition, illustrates applications with many problems, and requires only minimal prerequisites of multidimensional calculus and basic complex variables. The author clearly presents ideas, precise theorem statements, and explanations of the proofs.

Abstract

This book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudo-differential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book. in applied analysis and mathematical physics.