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Classical Fourier Transforms

Author: Komaravolu Chandrasekharan
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 1989.
Series: Universitext.
Edition/Format:   eBook : Bibliographic data : EnglishView all editions and formats
Summary:
This book gives a thorough introduction on classical Fourier transforms in a compact and self-contained form. Chapter I is devoted to the L1-theory: basic properties are proved as well as the Poisson summation formula, the central limit theorem and Wiener's general tauberian theorem. As an illustraiton of a Fourier transformation of a function not belonging to L1 ( -,) an integral due to Ramanujan is given. Chapter  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Bibliographic data, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Komaravolu Chandrasekharan
ISBN: 9783642740299 3642740294 9783540502487 3540502483
OCLC Number: 840295200
Description: 1 online resource (VII, 172 pages).
Contents: Fourier transforms on L1( -,) --
Fourier transforms on L2( -,) --
Fourier-Stieltjes transforms (one variable) --
Notes --
References.
Series Title: Universitext.
Responsibility: by Komaravolu Chandrasekharan.

Abstract:

This book gives a thorough introduction on classical Fourier transforms in a compact and self-contained form. Chapter I is devoted to the L1-theory: basic properties are proved as well as the Poisson summation formula, the central limit theorem and Wiener's general tauberian theorem. As an illustraiton of a Fourier transformation of a function not belonging to L1 ( -,) an integral due to Ramanujan is given. Chapter II is devoted to the L2-theory, including Plancherel's theorem, Heisenberg's inequality, the Paley-Wiener theorem, Hardy's interpolation formula and two inequalities due to Bernstein. Chapter III deals with Fourier-Stieltjes transforms. After the basic properties are explained, distribution functions, positive-definite functions and the uniqueness theorem of Offord are treated. The book is intended for undergraduate students and requires of them basic knowledge in real and complex analysis.

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