Note on basic features of large time behaviour of heat kernels
-
Matthias Keller
,
Daniel Lenz
Abstract
Large time behaviour of heat semigroups (and, more generally, of positive selfadjoint semigroups) is studied. Convergence of the semigroup to the ground state and of averaged logarithms of kernels to the ground state energy is shown in the general framework of positivity improving selfadjoint semigroups. This framework encompasses all irreducible semigroups coming from Dirichlet forms as well as suitable perturbations thereof. It includes, in particular, Laplacians on connected manifolds, metric graphs and discrete graphs.
Funding source: FCT
Award Identifier / Grant number: SFRH/BPD/45419/2008/
Funding source: FCT
Award Identifier / Grant number: PTDC/MAT/101007/2008
Funding source: German Research Foundation (DFG)
It is our great pleasure to acknowledge fruitful and stimulating discussions with Józef Dodziuk on the topics discussed in the paper. R. Wojciechowski would like to thank Isaac Chavel and Leon Karp for introducing him to the subject and for their continued encouragement and support.
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- The length metric on the set of orthogonal projections and new estimates in the subspace perturbation problem
- A Giambelli formula for even orthogonal Grassmannians
- Lifting in Frattini covers and a characterization of finite solvable groups
- Note on basic features of large time behaviour of heat kernels
- A decomposition theorem in II1-factors
- Wonderful resolutions and categorical crepant resolutions of singularities
- Tannaka–Kreĭn duality for compact quantum homogeneous spaces II. Classification of quantum homogeneous spaces for quantum SU(2)
- An approach of the minimal model program for horospherical varieties via moment polytopes
- Height of exceptional collections and Hochschild cohomology of quasiphantom categories
Articles in the same Issue
- Frontmatter
- The length metric on the set of orthogonal projections and new estimates in the subspace perturbation problem
- A Giambelli formula for even orthogonal Grassmannians
- Lifting in Frattini covers and a characterization of finite solvable groups
- Note on basic features of large time behaviour of heat kernels
- A decomposition theorem in II1-factors
- Wonderful resolutions and categorical crepant resolutions of singularities
- Tannaka–Kreĭn duality for compact quantum homogeneous spaces II. Classification of quantum homogeneous spaces for quantum SU(2)
- An approach of the minimal model program for horospherical varieties via moment polytopes
- Height of exceptional collections and Hochschild cohomology of quasiphantom categories
