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Strongly Continuous Semigroups and Stochastic Representation
Author(s) -
Liu Genqian
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610701003003
Subject(s) - mathematics , representation (politics) , bounded function , elliptic operator , order (exchange) , boundary (topology) , convergence (economics) , pure mathematics , kernel (algebra) , mathematical analysis , finance , politics , political science , law , economics , economic growth
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.