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MR1797661 (2002b:31012) 31C25 (35B05 35K05 47D07)
Bendikov, A.; Saloff-Coste, L. On- and off-diagonal heat kernel behaviors on certain infinite dimensional local Dirichlet spaces. Amer. J. Math. 122 (2000), no. 6, 1205–1263.
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