文章基本信息

标题：Jordan decomposition and geometric multiplicity for a class of non-symmetric Ornstein-Uhlenbeck operators
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作者：Yulei Rao ; Jiying Wang ; Yong Chen 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2014
卷号：2014
期号：1
页码：34
DOI：10.1186/1687-1847-2014-34
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we calculate the Jordan decomposition for a class of non-symmetric Ornstein-Uhlenbeck operators with the drift coefficient matrix, being a Jordan block, and the diffusion coefficient matrix, being the identity multiplying a constant. For the 2-dimensional case, we present all the general eigenfunctions by mathematical induction. For the 3-dimensional case, we divide the calculation of the Jordan decomposition into three steps. The key step is to do the canonical projection onto the homogeneous Hermite polynomials, and then use the theory of systems of linear equations. Finally, we get the geometric multiplicity of the eigenvalue of the Ornstein-Uhlenbeck operator.
关键词：Jordan decomposition ; 2-dimensional non-symmetric Ornstein-Uhlenbeck operator ; 3-dimensional non-symmetric Ornstein-Uhlenbeck operator