Abstract
Abstract : A large number of properties which are peculiar to symmetric Markov semigroups stem from the fact that such semigroups can be analyzed simultaneously by Hilbert space techniques as well as techniques coming from maximum principle considerations. The feature of symmetric Markov semigroups in which this fact is most dramatically manifested is the central role played by the Dirichlet form. In particular, the Dirichlet form is a remarkably powerful tool with which to compare symmetric Markov semigroups. The present paper consists of a number of examples which illustrate this point. There exist tight relationships between uniform decay estimates on the semigroup and certain Sobolev like inequalities involving the Dirichlet form.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
