A NOTE ON THE ESSENTIAL SELF-ADJOINTNESS OF ORNSTEIN–UHLENBECK OPERATORS PERTURBED BY A DISSIPATIVE DRIFT AND A POTENTIAL

DOI10.1142/S0219025704001621zbMath1087.47049OpenAlexW1998630821MaRDI QIDQ5315824

Isabel Simão, Hongwei Long

Publication date: 9 September 2005

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219025704001621

zbMATH Keywords

essential self-adjointnessapproximation criterionperturbed Ornstein-Uhlenbeck operator

Mathematics Subject Classification ID

Dirichlet forms (31C25) Diffusion processes (60J60) General theory of partial differential operators (47F05) Applications of operator theory in probability theory and statistics (47N30)

Cites Work

• Self-adjointness of elliptic operators with infinitely many variables
• Dirichlet operators: A priori estimates and the uniqueness problem
• Infinite-dimensional Dirichlet operators. I: Essential selfadjointness and associated elliptic equations
• Dirichlet operators via stochastic analysis
• Regularity of invariant measures on finite and infinite dimensional spaces and applications
• An example of regular \((r,p)\)-capacity and essential self-adjointness of a diffusion operator in infinite dimensions
• Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators
• On the self-adjointness of differential operators with finitely or infinitely many variables, and evolution equations
• Kato's inequality and essential self-adjointness of dirichlet operators on certain banach spaces
• On uniqueness of invariant measures for finite- and infinite-dimensional diffusions
• DIRICHLET OPERATORS WITH VARIABLE COEFFICIENTS IN L^p-SPACES OF FUNCTIONS OF INFINITELY MANY VARIABLES COEFFICIENTS
• Ergodicity for Infinite Dimensional Systems

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