Homogeneity in generalized function algebras

Details Homogeneity in generalized function algebras Homogeneity in generalized function algebras

2006-11-13

arxiv.org/abs/math/0611377v2

J. Math. Anal. Appl. 339 (2008), pp. 889-904.

Mathematics

General Mathematics

24 pages, reorganized, extended introduction

Scientific paper

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.

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