Geodesic
A Pettis-type integral and applications to transition semigroups
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 2, pp. 437-459
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Motivated by applications to transition semigroups, we introduce the notion of a norming dual pair and study a Pettis-type integral on such pairs. In particular, we establish a sufficient condition for integrability. We also introduce and study a class of semigroups on such dual pairs which are an abstract version of transition semigroups. Using our results, we give conditions ensuring that a semigroup consisting of kernel operators has a Laplace transform which also consists of kernel operators. We also provide conditions under which a semigroup is uniquely determined by its Laplace transform.
Motivated by applications to transition semigroups, we introduce the notion of a norming dual pair and study a Pettis-type integral on such pairs. In particular, we establish a sufficient condition for integrability. We also introduce and study a class of semigroups on such dual pairs which are an abstract version of transition semigroups. Using our results, we give conditions ensuring that a semigroup consisting of kernel operators has a Laplace transform which also consists of kernel operators. We also provide conditions under which a semigroup is uniquely determined by its Laplace transform.
DOI : 10.1007/s10587-011-0065-3
Classification : 46G10, 47D06, 60J35
Keywords: Pettis-type integral; dual pairs; Laplace transform; transition semigroup 
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Kunze, Markus. A Pettis-type integral and applications to transition semigroups. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 2, pp. 437-459. doi: 10.1007/s10587-011-0065-3

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