Integration and microlocal analysis in Colombeau algebras of generalized functions

被引：16
|
作者：
Hörmann, G [1 ]
机构：
[1] Univ Vienna, Inst Math, A-1090 Vienna, Austria
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 1999年 / 239卷 / 02期
关键词：
D O I：
10.1006/jmaa.1999.6565
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study integration and Fourier transform in the Colombeau algebra G(T) of tempered generalized functions using a general damping factor. This unifies different settings described earlier by J. F. Colombeau, M. Nedeljikov, S. Pilipovic, and M. Damsma (for a simplified version). Further we prove characterizations of regularity for generalized functions in two situations: compactly supported or in the image of T' inside G(T). Finally we investigate the notion of wave front set in the Colombeau algebra G(Omega), Omega an open subset of R-n, and show that it is in fact independent of the damping measure used for Fourier transform. (C) 1999 Academic Press.
引用
收藏
页码：332 / 348
页数：17
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