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Journal of the London Mathematical Society 2002 65(3):639-660; doi:10.1112/S0024610701003003
© 2002 by London Mathematical Society
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© The London Mathematical Society

Strongly Continuous Semigroups and Stochastic Representation

Genqian Liu

Department of Mathematics, Beijing Normal University Beijing 100875, China
School of Mathematical Sciences, Peking University China

Received 5 May 2000. Revision received 16 July 2001.

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.

Department of Mathematics, Beijing Institute of Technology, China


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