Introduction to Fourier analysis and generalised functions

by M.J. Lighthill

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.

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  • 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.

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書名 Introduction to Fourier analysis and generalised functions
著作者等 Lighthill, M. J., Sir
Ablowitz Mark J.
Davis S.H.
Hinch E. J.
Iserles A.
Ockendon J.
Olver P.J.
Lighthill M. J.
書名別名 Fourier analysis and generalised functions

An introduction to Fourier analysis and generalised functions
シリーズ名 Cambridge monographs on mechanics and applied mathematics
出版元 Cambridge University Press
刊行年月 1958
ページ数 viii, 79 p.
大きさ 22 cm
ISBN 0521091284
NCID BA00464388
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言語 英語
出版国 イギリス