Classical Fourier Transforms (Universitext) - Softcover

Chandrasekharan, Komaravolu

Softcover

ISBN 10: 3540502483 ISBN 13: 9783540502487

Publisher: Springer, 1988

Synopsis

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.

Edition details

• Publisher: Springer
• Publication date: 1988
• Language: English
• ISBN 10: 3540502483
• ISBN 13: 9783540502487
• Binding: Paperback
• Number of pages: 179