An Introduction to Fourier Analysis and Generalised Functions (Cambridge Monographs on Mechanics)

Lighthill, M. J.

Cambridge University Press（1958/01発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 108 p.
• 言語 ENG
• 商品コード 9780521091282
• DDC分類 515.723

Full Description

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.

Contents

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.