Vol. 20, No. 1, 1967

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Asymptotic expansions of Fourier transforms and discrete polyharmonic Green’s functions

Moshe Mangad

Vol. 20 (1967), No. 1, 85–98

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