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Fourier transforms and harmonic functions

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  09 April 2009

N. Ormerod
N. Ormerod
Affiliation:
Department of Mathematics University of North South WalesKensington, N.S.W. 2033, Australia
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Abstract

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The purpose of this paper is to present a novel proof of a well-known relationship between functions in harmonic subspaces of L2(Rn) ∪ L1 (Rn) and their Fourier transforms. The proof uses a characterisation of spherical harmonics given by Hecke and a method developed by the author in a previous paper.

Keywords

Fourier transformspherical harmonicszeta function.

MSC classification

Secondary: 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 36 , Issue 2 , April 1984 , pp. 187 - 193
Copyright
Copyright © Australian Mathematical Society 1984

References

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[3]Muller, C., Spherical harmonics, Springer-Verlag Lecture Notes 17 (Springer-Verlag, Berlin).CrossRefGoogle Scholar
[4]Ormerod, N., ‘Fourier transforms of radial functions’, J. Math. Anal. Appl. 69 (1979), 559–562.CrossRefGoogle Scholar
[5]Schoeneberg, B., Elliptic modular functions (Springer-Verlag, Berlin, 1974).CrossRefGoogle Scholar
[6]Stein, E. and Weiss, G., Inroduction to Fourier analysis on Euclidean spaces (Princeton Univ. Press, Princeton, N. J., 1971).Google Scholar