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Lectures on integral transforms

Author: N I Akhiezer
Publisher: Providence, R.I. : American Mathematical Society, ©1988.
Series: Translations of mathematical monographs, v. 70.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Akhiezer, N.I. (Naum Ilʹich), 1901-1980.
Lectures on integral transforms.
Providence, R.I. : American Mathematical Society, ©1988
(DLC) 88019393
(OCoLC)18134534
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: N I Akhiezer
ISBN: 9781470444846 1470444844
OCLC Number: 1031944773
Description: 1 online resource
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
Series Title: Translations of mathematical monographs, v. 70.
Other Titles: Lekt︠s︡ii ob integralʹnykh preobrazovanii︠a︡kh.
Responsibility: N.I. Akhiezer ; [translated from the Russian by H.H. McFaden ; translation edited by Ben Silver].

Abstract:

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-Planchere.

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