N.I. Akhiezer – författare

This book contains a systematic presentation of the theory of elliptic functions and some of its applications. A translation from the Russian, this book is intended primarily for engineers who work with elliptic functions. It should be accessible to those with background in the elements of mathematical analysis and the theory of functions contained in approximately the first two years of mathematics and physics courses at the college level.

This book, which grew out of lectures given over the course of several years at Kharkov University for students in the Faculty of Mechanics and Mathematics, is devoted to classical integral transforms, principally the Fourier transform, and their applications. The author develops the general theory of the Fourier transform for the space $L^1(E_n)$ of integrable functions of $n$ variables. His proof of the inversion theorem is based on the general Bochner theorem on integral transforms, a theorem having other applications within the subject area of the book. The author also covers Fourier-Plancherel theory in $L^2(E_n)$. In addition to the general theory of integral transforms, connections are established with other areas of mathematical analysis - such as the theory of harmonic and analytic functions, the theory of orthogonal polynomials, and the moment problem - as well as to mathematical physics.