2012/12/09 by Yong Chen, Ying Li, Chen, Yong +1
Computer Science · Mathematics · #33C45 #47A75 #47F05 #60H99 #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Probability (math.PR) #Spectral Theory in Mathematical Physics #math.FA #math.PR #msc:33C45 #msc:47A75 #msc:47F05 #msc:60H99
paper · pdf · doi:10.48550/arxiv.1212.1852
openalex publication_date 2012/12/09 · arxiv created 2013/02/20 · arxiv updated 2013/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we calculate the Jordan decomposition (or say, the Jordan canonical form) for a class of non-symmetric Ornstein-Uhlenbeck operators with the drift coefficient matrix being a Jordan block and the diffusion coefficient matrix being identity multiplying a constant. For the 2-dimensional case, we present all the general eigenfunctions by the induction. For the 3-dimensional case, we divide the calculating of the Jordan decomposition into several steps (the key step is to do the canonical projection onto the homogeneous Hermite polynomials, next we use the theory of systems of linear equations). As a by-pass product, we get the geometric multiplicity of the eigenvalue of the Ornstein-Uhlenbeck operator.