Gaussian heat kernel upper bounds via the Phragmén–Lindelöf theorem

By T. Coulhon, Adam S. Sikora. 2006

215 citations recorded by the source corpus.

We prove that in the presence of L2 Gaussian estimates, the so‐called Davies–Gaffney estimates, on‐diagonal upper bounds imply precise off‐diagonal Gaussian upper bounds for the kernels of analytic families of operators on metric measure spaces.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c34dce6ed92f3e4974615fd901bb79ec010484fa

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In Applied Mathematics

1. S. Hofmann
2. M. Mitrea
3. T. Coulhon
4. Lixin Yan
5. D. Mitrea
6. Gerard Kerkyacharian
7. Xuan Thinh Duong
8. Dachun Yang

In Mathematical Physics

1. S. Hofmann
2. Lixin Yan
3. Gerard Kerkyacharian
4. D. Mitrea
5. T. Coulhon
6. M. Mitrea
7. G. Lu
8. Xuan Thinh Duong

Citations in the corpus

• Heat Kernel Generated Frames in the Setting of Dirichlet Spaces (2012, background): “One can see that by combining the results in [9, 45] and [13], this estimate and the doubling condition (1.”
• Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates (2011, methodology): “Proof. For the proof, we refer the reader to Theorem 2 in [Si2] and Theorem 3.4 in [ CS ].”