Vol. 20, No. 1, 1967

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ISSN: 0030-8730
Asymptotic expansions of Fourier transforms and discrete polyharmonic Green’s functions

Moshe Mangad

Vol. 20 (1967), No. 1, 85–98
DOI: 10.2140/pjm.1967.20.85

The results in M. J. Lighthill’s book, Fourier Analysis and Generalized Functions, dealing with the asymptotic developments of Fourier transforms and Fourier series coefficients, are extended to the n-dimensional case. Together wilh several theorems due to L. Schwartz’s work on distribution theory, integral representations and asymptotic developments of the n-dimensional discrete (generalized) polyharmonic Green’s functions, are then obtained. A few examples of these Green’s functions are illustrated and compared with knuwn results.

Mathematical Subject Classification
Primary: 42.25
Received: 8 July 1965
Published: 1 January 1967
Moshe Mangad