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Gaussian heat kernel upper bounds via the Phragmén–Lindelöf theorem
Author(s) -
Coulhon Thierry,
Sikora Adam
Publication year - 2008
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdm050
Subject(s) - mathematics , diagonal , heat kernel , gaussian , metric (unit) , upper and lower bounds , kernel (algebra) , measure (data warehouse) , combinatorics , gaussian function , pure mathematics , discrete mathematics , mathematical analysis , geometry , operations management , physics , quantum mechanics , database , computer science , economics
We prove that in the presence of L 2 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.