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STRONGLY CONTINUOUS SEMIGROUPS AND STOCHASTIC REPRESENTATION

Published online by Cambridge University Press:  24 March 2003

GENQIAN LIU
GENQIAN LIU
Affiliation:
Department of Mathematics, Beijing Normal University, Beijing 100875, China School of Mathematical Sciences, Peking University, China Current address: Department of Mathematics, Beijing Institute of Technology, China
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Abstract

Second-order elliptic operators realized under Dirichlet boundary conditions in bounded domains are shown to generate strongly continuous semigroups in the topology of uniform convergence. The stochastic representation and integral representation with kernel for the strongly continuous semigroups are given. Furthermore, several useful formulae for the principal eigenvalue of second-order elliptic operators are obtained.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 65 , Issue 3 , June 2002 , pp. 639 - 660
Copyright
The London Mathematical Society, 2002

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