We introduce a new class of weakly continuous semigroups and give a characterization of their infinitesimal generators, generalizing the classical Hille-Yosida Theorem for strongly continuous semigroups. The results are illustrated by the example of transition semigroups corresponding to the solutions of certain stochastic differential equations.
A Hille-Yosida theorem for weakly continuous semigroups / S. CERRAI. - In: SEMIGROUP FORUM. - ISSN 0037-1912. - STAMPA. - 49:(1994), pp. 349-367. [10.1007/BF02573496]
A Hille-Yosida theorem for weakly continuous semigroups
CERRAI, SANDRA
1994
Abstract
We introduce a new class of weakly continuous semigroups and give a characterization of their infinitesimal generators, generalizing the classical Hille-Yosida Theorem for strongly continuous semigroups. The results are illustrated by the example of transition semigroups corresponding to the solutions of certain stochastic differential equations.
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