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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Application of the sector condition to the classification of sub-Markovian semigroups

Author: Martin L. Silverstein
Journal: Trans. Amer. Math. Soc. 244 (1978), 103-146
MSC: Primary 60J50
MathSciNet review: 506612
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Abstract: Let $ {p_{t}}$, $ t > 0$, be a strongly continuous submarkovian semigroup on a real Hilbert space $ {L^2}(X, m)$. The measure m is assumed to be excessive and the $ {L^2}$ generator A is assumed to satisfy an estimate (the sector condition) which permits the application of Dirichlet spaces (not necessarily symmetric). Other submarkovian semigroups $ P_t^ \sim $ with the same local generator and cogenerator and relative to which m is again excessive are classified in terms of generators for processes which live on a suitable boundary.

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Keywords: Submarkovian, Dirichlet spaces, sector condition, boundary generation
Article copyright: © Copyright 1978 American Mathematical Society

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