Abstract
We derive the off-diagonal short-time asymptotics of the heat kernels of functions of generalised Laplacians on a closed manifold. As an intermediate step we give an explicit asymptotic series for the kernels of the complex powers of generalised Laplacians. Each asymptotic series is formulated in terms of the geodesic distance. The key application concerns upper bounds for the transition density of subordinate Brownian motion. The approach is highly explicit and tractable.
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Fahrenwaldt, M.A. Off-Diagonal Heat Kernel Asymptotics of Pseudodifferential Operators on Closed Manifolds and Subordinate Brownian Motion. Integr. Equ. Oper. Theory 87, 327–347 (2017). https://doi.org/10.1007/s00020-017-2344-3
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DOI: https://doi.org/10.1007/s00020-017-2344-3
Mathematics Subject Classification
- Primary 35K08
- Secondary 58J65
- 35S05
Keywords
- Pseudodifferential operators
- Complex powers
- Heat kernel
- Mellin transform
- Subordinate Brownian motion