Lectures on integral transforms
Author(s)
Bibliographic Information
Lectures on integral transforms
(Translations of mathematical monographs, v. 70)
American Mathematical Society, c1988
- Other Title
-
Lekt︠s︡ii ob integralʹnykh preobrazovanii︠a︡kh
Available at 52 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Translation of: Lekt︠s︡ii ob integralʹnykh preobrazovanii︠a︡kh
Description and Table of Contents
Description
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.
Table of Contents
Averaging operators and the Bochner theorem The Fourier transform in $L^1$ The inversion theorem in $L^1$. The Poisson integral Harmonic functions. The Dirichlet problem for a ball and a half-space The Fourier transform in $L^2$ Hermite functions Spherical functions Positive definite functions The Hankel transform Orthogonal polynomials and the moment problem The class $H^2$. The Paley-Wiener theorem Boundary properties of functions analytic in the upper half-plane and the Hilbert transform The Poisson summation formula and some of its applications Applications of the Laplace and Fourier transforms to the solution of boundary value problems in mathematical physics Fourier transforms of increasing functions. The Wiener-Hopf technique.
by "Nielsen BookData"