ENGLISH

Classical Fourier Transforms

By Komaravolu Chandrasekharan (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1989
ISBN
978-3-540-50248-7, 978-3-642-74029-9
DOI
10.1007/978-3-642-74029-9
Language
english
Format
PDF
Filesize
5 MB (5184041 bytes)
Series
Universitext
Edition
1
Pages
172\177
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Real Functions; Probability Theory and Stochastic

Description

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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