A Pettis-type integral and applications to transition semigroups

Markus Kunze

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 2, page 437-459
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Kunze, Markus. "A Pettis-type integral and applications to transition semigroups." Czechoslovak Mathematical Journal 61.2 (2011): 437-459. <http://eudml.org/doc/196928>.

@article{Kunze2011,
abstract = {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.},
author = {Kunze, Markus},
journal = {Czechoslovak Mathematical Journal},
keywords = {Pettis-type integral; dual pairs; Laplace transform; transition semigroup; Pettis-type integral; dual pairs; Laplace transform; transition semigroup},
language = {eng},
number = {2},
pages = {437-459},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A Pettis-type integral and applications to transition semigroups},
url = {http://eudml.org/doc/196928},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Kunze, Markus
TI - A Pettis-type integral and applications to transition semigroups
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 2
SP - 437
EP - 459
AB - 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.
LA - eng
KW - Pettis-type integral; dual pairs; Laplace transform; transition semigroup; Pettis-type integral; dual pairs; Laplace transform; transition semigroup
UR - http://eudml.org/doc/196928
ER -

References

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