An Introduction to Fourier Analysis and Generalised Functions

M. J. Lighthill (Author)

9780521091282, Cambridge University Press

Paperback / softback, published 1 January 1958

108 pages
21.6 x 13.5 x 1.4 cm, 0.15 kg

'Clearly and attractively written, but without any deviation from rigorous standards of mathematical proof … the book should be well within the compass of an honours student in mathematics or theoretical physics, and they are most strongly urged to buy it and read it.' Science Progess

This monograph on generalised functions, Fourier integrals and Fourier series is intended for readers who, while accepting that a theory where each point is proved is better than one based on conjecture, nevertheless seek a treatment as elementary and free from complications as possible. Little detailed knowledge of particular mathematical techniques is required; the book is suitable for advanced university students, and can be used as the basis of a short undergraduate lecture course. A valuable and original feature of the book is the use of generalised-function theory to derive a simple, widely applicable method of obtaining asymptotic expressions for Fourier transforms and Fourier coefficients.

1. Introduction
2. The theory of generalised functions and their Fourier transforms
3. Definitions, properties and Fourier transforms of particular generalised functions
4. The asymptotic estimation of Fourier transforms
5. Fourier series
Index.

Subject Areas: Functional analysis & transforms [PBKF]