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- W820704113 abstract "Let E be a second countable locally compact Hausdorff space and let L be a linear operator with domain D(L) and range R(L) in C 0 (E) = Co (E, R). Suppose that the operator L satisfies the maximum principle and that L possesses the Korovkin property in the sense that there exists a strictly positive real number t0 > 0 such that for every ({{x}_{0}} in E cup { Delta }) the equality $$ begin{gathered} mathop {inf }limits_{h in D(L)} mathop {sup }limits_{x in E} left{ {h({x_0}) + left[ {g - left( {I - {t_0}L} right)h} right]left( x right)} right} hfill = mathop {sup }limits_{h in D(L)} mathop {inf }limits_{x in E} left{ {h({x_0}) + left[ {g - left( {I - {t_0}L} right)h} right]left( x right)} right} hfill end{gathered} $$is valid for all g∈ C0 (E). Suppose that the domain D (L) is dense in C0 (E). Then the operator L extends in a unique fashion to the generator of a Feller semigroup. Moreover, for every x∈ E the martingale problem is well-posed for the operator L." @default.
- W820704113 created "2016-06-24" @default.
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- W820704113 date "2000-01-01" @default.
- W820704113 modified "2023-09-25" @default.
- W820704113 title "On the Korovkin Property and Feller Semigroups" @default.
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- W820704113 doi "https://doi.org/10.1007/978-1-4612-1372-7_10" @default.
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