On the eigenfunctions of the complex Ornstein-Uhlenbeck operators

被引：11

作者：

Chen, Yong ^{[1
]}

Liu, Yong ^{[2
]}

机构：

[1] Hunan Univ Sci & Technol, Sch Math & Comp Sci, Xiangtan 411201, Hunan, Peoples R China

[2] Peking Univ, Sch Math Sci, LMAM, Ctr Stat Sci, Beijing 100871, Peoples R China

来源：

KYOTO JOURNAL OF MATHEMATICS | 2014年 / 54卷 / 03期

基金：

美国国家科学基金会;

关键词：

SEMIGROUPS; SPECTRUM; RESPECT; SPACES;

D O I：

10.1215/21562261-2693451

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Starting from the 1-dimensional complex-valued Ornstein-Uhlenbeck process, we present two natural ways to obtain the associated eigenfunctions of the 2-dimensional normal Ornstein-Uhlenbeck operator in the complex Hilbert space L-C(2)(mu) We call the eigenfunctions Hermite-Laguerre-It (o) over cap polynomials. In addition, the Mehler summation formula for the complex process is shown.

引用

页码：577 / 596

页数：20

共 24 条

[1]

Balescu R., 1997, STATISTICAL DYNAMICS: Matter Out of Equilibrium

[2] Symmetric Ornstein-Uhlenbeck semigroups and their generators [J].

Chojnowska-Michalik, A ;

Goldys, B .

PROBABILITY THEORY AND RELATED FIELDS, 2002, 124 (04) :459-486

[3] Nonsymmetric Ornstein-Uhlenbeck semigroup as second quantized operator [J].

ChojnowskaMichalik, A ;

Goldys, B .

JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 1996, 36 (03) :481-498

[4]

Conway R. A., 1990, GRAD TEXTS MATH, V96

[5]

Courant R., 1966, METHODS MATH PHYS, V1

[6]

Horn R.A., 2012, Matrix analysis, DOI [10.1017/CBO9780511810817, DOI 10.1017/CBO9780511810817]

[7]

Ito K., 1952, JAPAN J MATH, V22, P63

[8]

Ito Kiyosi, 1951, J. Math. Soc. Japan, V3, P157, DOI 10.2969/jmsj/00310157

[9]

Janson S., 1997, Gaussian Hilbert Spaces, DOI 10.1017/CBO9780511526169

[10] L1-spectrum of Banach space valued Ornstein-Uhlenbeck operators [J].

Kozhan, Rostyslav V. .

SEMIGROUP FORUM, 2009, 78 (03) :547-553

← 1 2 3 →