A characterization of real matrix semigroups

2023/05/24 by Benedict Bauer, Stefan Gerhold, Bauer, Benedict +1
Computer Science · Mathematics · #15A16 #39B22 #47D03 #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Probability (math.PR) #Random Matrices and Applications #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2305.15522

openalex publication_date 2023/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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