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Some inequalities for sub-Markovian generators and their applications to the perturbation theory


Authors: V. A. Liskevich and Yu. A. Semenov
Journal: Proc. Amer. Math. Soc. 119 (1993), 1171-1177
MSC: Primary 47D07; Secondary 47A55, 47B25, 47F05
DOI: https://doi.org/10.1090/S0002-9939-1993-1160303-9
MathSciNet review: 1160303
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Abstract: We characterize the domain in $ {L^p}$-space of generators of submarkovian semigroups in terms of the form domain in $ {L^2}$ and give the corresponding inequality. Using this inequality we obtain a criterion for the formal difference $ A - B$ of such generators to be a generator of a contraction semigroup in $ {L^p}$. The conditions on perturbation are expressed in terms of forms, i.e., in $ {L^2}$-terms.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1160303-9
Keywords: Submarkovian semigroups, form-bounded perturbations
Article copyright: © Copyright 1993 American Mathematical Society

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