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

Abstract

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

Milestones

Received: 8 July 1965

Published: 1 January 1967