Fourier transform in bounded domains
type: Item
instance of: scholarly article
title: Fourier transform in bounded domains
zbMATH Open document ID: 0971.46025
DOI: 10.1023/A:1004262406344
published in: Meccanica
publication date: 2000-08-27T00:00:00Z
review text: The author maintains that the concept of Schwartz distributions and their extension to ultra distributions of Gelfand and Shilov, enable one to find, by means of the Fourier transform, a second `language' to characterize physical behaviour. The author also maintains that almost any expression with physical meaning, can be transformed even if it is formulated in domains with complicated boundaries and even if it is not integrable. It is also stated that numerical procedures in the transformed space can be developed in analogy to those well-known in engineering mechanics like the methods of finite or boundary elements. In addition, the author maintains that the concept of the characteristic distribution leads to a very simple derivation of the Green-Gauss formulas for the boundary or finite elements [\textit{L. Hörmander}, ``The analysis of linear partial differential operators'', Vol. I--IV, Berlin, Heidelberg (1983; Zbl 0521.35001, Zbl 0521.35002) and (1985; Zbl 0601.35001, Zbl 0612.35011)].
Mathematics Subject Classification ID: 46F12
Mathematics Subject Classification ID: 46F20
Mathematics Subject Classification ID: 46F10
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74K15
zbMATH DE Number: 1093028
zbMATH Keywords: Schwartz distributions
zbMATH Keywords: ultra distributions
zbMATH Keywords: Fourier transform
zbMATH Keywords: methods of finite or boundary elements
zbMATH Keywords: characteristic distribution
zbMATH Keywords: Green-Gauss formulas
author: Fabian M. E. Duddeck
reviewed by: Gandikota L. N. Rao
MaRDI profile type: Publication
full work available at URL: a:1004262406344
OpenAlex ID: W111775195
description: scientific article; zbMATH DE number 1093028