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

Silverstein, Martin L.

doi:10.1090/S0002-9947-1978-0506612-1

Application of the sector condition to the classification of sub-Markovian semigroups
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by Martin L. Silverstein

Trans. Amer. Math. Soc. 244 (1978), 103-146

DOI: https://doi.org/10.1090/S0002-9947-1978-0506612-1

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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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Measures associées à une forme de Dirichlet

Measures associées à une forme de Dirichlet-Applications