Group invariant Colombeau generalized functions
Functional Analysis
2017-05-24 v2 Analysis of PDEs
Abstract
Colombeau generalized functions invariant under smooth (additive) one-parameter groups are characterized. This characterization is applied to generalized functions invariant under orthogonal groups of arbitrary signature, such as groups of rotations or the Lorentz group. Further, a one-dimensional Colombeau generalized function with two (real) periods is shown to be a generalized constant, when the ratio of the periods is an algebraic nonrational number. Finally, a nonstandard Colombeau generalized function invariant under standard translations is shown to be constant.
Cite
@article{arxiv.math/0512219,
title = {Group invariant Colombeau generalized functions},
author = {Hans Vernaeve},
journal= {arXiv preprint arXiv:math/0512219},
year = {2017}
}
Comments
16 pages; extended content