Volumes I through V of Theorems and Problems in Functional Analysis: The Answer Book present different techniques for solving the 828 Exercises found in the A.A. Kirillov and Gvichiani book, entitled Theorems and Problems in Functional Analysis. The original book by Kirillov and Gvichiani was in the Problem Book in Mathematics Series, published by Springer.

This volume focuses on the Fourier transform and basic Harmonic Analysis.  Key topics include:

-convolution products over a group,

-characters,

-Fourier transform,

-Fourier series,

-Fourier integral,

-the Paley-Wiener theorem, and

-the Fourier transform of distributions.

Supplementing the book, Theorems and Problems in Functional Analysis, these volumes may be used by graduate students taking a course in functional analysis.  In order to understand this text, the reader must be familiar with mathematical analysis and real analysis.