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A Pettis-type integral and applications to transition semigroups

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2012

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https://doi.org/10.1007/s10587-011-0065-3
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Czechoslovak Mathematical Journal. 2012, 61(2), pp. 437-459. ISSN 0011-4642. eISSN 1572-9141. Available under: doi: 10.1007/s10587-011-0065-3

Zusammenfassung

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.

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Fachgebiet (DDC)
510 Mathematik

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Pettis-type integral, dual pairs, Laplace transform, transition semigroup

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ISO 690KUNZE, Markus, 2012. A Pettis-type integral and applications to transition semigroups. In: Czechoslovak Mathematical Journal. 2012, 61(2), pp. 437-459. ISSN 0011-4642. eISSN 1572-9141. Available under: doi: 10.1007/s10587-011-0065-3
BibTex
@article{Kunze2012-02-09Petti-41255,
  year={2012},
  doi={10.1007/s10587-011-0065-3},
  title={A Pettis-type integral and applications to transition semigroups},
  number={2},
  volume={61},
  issn={0011-4642},
  journal={Czechoslovak Mathematical Journal},
  pages={437--459},
  author={Kunze, Markus}
}
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