A characterization of real matrix semigroups
Rings and Algebras
2023-05-26 v1 Probability
Abstract
We characterize all real matrix semigroups satisfying a mild boundedness assumption, without assuming continuity. Besides the continuous solutions of the semigroup functional equation, we give a description of solutions arising from non-measurable solutions of Cauchy's functional equation. To do so, we discuss the primary decomposition and the Jordan-Chevalley decomposition of a matrix semigroup. Our motivation stems from a characterization of all multi-dimensional self-similar Gaussian Markov processes, which is given in a companion paper.
Cite
@article{arxiv.2305.15522,
title = {A characterization of real matrix semigroups},
author = {Benedict Bauer and Stefan Gerhold},
journal= {arXiv preprint arXiv:2305.15522},
year = {2023}
}