Homogeneity in generalized function algebras
General Mathematics
2008-02-13 v2
Abstract
We investigate homogeneity in the special Colombeau algebra. It is shown that strongly scaling invariant functions on the d-dimensional space are simply the constants. On the pierced space, strongly homogeneous functions admit tempered representatives, whereas on the whole space, such functions are polynomials with generalized coefficients. We also introduce weak notions of homogeneity and show that these are consistent with the classical notion on the distributional level. Moreover, we investigate the relation between generalized solutions of the Euler differential equation and homogeneity.
Cite
@article{arxiv.math/0611377,
title = {Homogeneity in generalized function algebras},
author = {Clemens Hanel and Eberhard Mayerhofer and Stevan Pilipovic and Hans Vernaeve},
journal= {arXiv preprint arXiv:math/0611377},
year = {2008}
}
Comments
24 pages, reorganized, extended introduction