Some results about dissipativity of Kolmogorov operators

Giuseppe Da Prato; Luciano Tubaro

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 4, page 685-699
  • ISSN: 0011-4642

Abstract

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Given a Hilbert space H with a Borel probability measure ν , we prove the m -dissipativity in L 1 ( H , ν ) of a Kolmogorov operator K that is a perturbation, not necessarily of gradient type, of an Ornstein-Uhlenbeck operator.

How to cite

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Prato, Giuseppe Da, and Tubaro, Luciano. "Some results about dissipativity of Kolmogorov operators." Czechoslovak Mathematical Journal 51.4 (2001): 685-699. <http://eudml.org/doc/30665>.

@article{Prato2001,
abstract = {Given a Hilbert space $H$ with a Borel probability measure $\nu $, we prove the $m$-dissipativity in $L^1(H, \nu )$ of a Kolmogorov operator $K$ that is a perturbation, not necessarily of gradient type, of an Ornstein-Uhlenbeck operator.},
author = {Prato, Giuseppe Da, Tubaro, Luciano},
journal = {Czechoslovak Mathematical Journal},
keywords = {Kolmogorov equations; invatiant measures; $m$-dissipativity; Kolmogorov equations; invatiant measures; -dissipativity},
language = {eng},
number = {4},
pages = {685-699},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some results about dissipativity of Kolmogorov operators},
url = {http://eudml.org/doc/30665},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Prato, Giuseppe Da
AU - Tubaro, Luciano
TI - Some results about dissipativity of Kolmogorov operators
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 4
SP - 685
EP - 699
AB - Given a Hilbert space $H$ with a Borel probability measure $\nu $, we prove the $m$-dissipativity in $L^1(H, \nu )$ of a Kolmogorov operator $K$ that is a perturbation, not necessarily of gradient type, of an Ornstein-Uhlenbeck operator.
LA - eng
KW - Kolmogorov equations; invatiant measures; $m$-dissipativity; Kolmogorov equations; invatiant measures; -dissipativity
UR - http://eudml.org/doc/30665
ER -

References

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  6. Uniqueness and Non-uniqueness of Semigroups Generated by Singular Diffusion Operators. Lecture Notes in Mathematics Vol. 1718, Springer-Verlag, Berlin, 1999. (1999) MR1734956
  7. 10.1006/jdeq.2000.3918, J. Differential Equations 173 (2001), 17–39. (2001) MR1836243DOI10.1006/jdeq.2000.3918
  8. Strong uniqueness for certain infinite-dimensional Dirichlet operators and applications to stochastic quantization, Ann. Scuola Norm. Sup. Pisa Cl. Sci.  (4) 27 (1999), 69–91. (1999) MR1658889
  9. Introduction to the Theory of (Non-Symmetric) Dirichlet Forms, Springer-Verlag, Berlin, 1992. (1992) MR1214375
  10. π -semigroups and applications. Preprint No.  9 of the Scuola Normale Superiore di Pisa, 1998. (1998) 

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