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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Some inequalities for sub-Markovian generators and their applications to the perturbation theory
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by V. A. Liskevich and Yu. A. Semenov PDF
Proc. Amer. Math. Soc. 119 (1993), 1171-1177 Request permission

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.
References
  • E. A. Carlen, S. Kusuoka, and D. W. Stroock, Upper bounds for symmetric Markov transition functions, Ann. Inst. H. Poincaré Probab. Statist. 23 (1987), no. 2, suppl., 245–287 (English, with French summary). MR 898496
  • Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
  • V. F. Kovalenko and Yu. A. Semenov, On the $L^p$-theory of Schrödinger semigroups. I, Ukrain. Mat. Zh. 41 (1989), no. 2, 273–278, 289 (Russian); English transl., Ukrainian Math. J. 41 (1989), no. 2, 246–249. MR 992836, DOI 10.1007/BF01060398
    • V. A. Liskevich, M. A. Perelmuter, and Yu. A. Semenov, Form-bounded perturbations of generators of submarkovian semigroups (in preparation). V. A. Liskevich and Yu. A. Semenov, One criterion of the essential self-adjointness of the Schrödinger operator, preprint, 1991.
  • Michael Reed and Barry Simon, Methods of modern mathematical physics. I. Functional analysis, Academic Press, New York-London, 1972. MR 0493419
  • Elias M. Stein, Topics in harmonic analysis related to the Littlewood-Paley theory. , Annals of Mathematics Studies, No. 63, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1970. MR 0252961
  • D. W. Stroock, An introduction to the theory of large deviations, Universitext, Springer-Verlag, New York, 1984. MR 755154, DOI 10.1007/978-1-4613-8514-1
  • N. Th. Varopoulos, Hardy-Littlewood theory for semigroups, J. Funct. Anal. 63 (1985), no. 2, 240–260. MR 803094, DOI 10.1016/0022-1236(85)90087-4
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • 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