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Central Gaussian Semigroups of Measures with Continuous Density by A. Bendikov; L. Saloff-Coste is a Mathematics article available to read on EtoBox.

This paper investigates the existence and properties of symmetric central Gaussian semigroups (m t ) t > 0 which are absolutely continuous and have a continuous density x W m t (x), t > 0, with respect to Haar measure on groups of the form R n × K where K is compact connected locally connected and has a countable basis for its topology. We prove that there always exists a wealth of such Gaussian semigroups on any such group. For instance, if k is any positive function increasing to infinity, there exists a symmetric central Gaussian semigroup having a continuous density such that log m t (e) [ log(1+1/t) k(1/t) as t tends to zero. Among other results of this type we give a necessary and sufficient condition on the structure of K for the existence of symmetric central Gaussian semigroups having a continuous density and such that t l log m t (e) is bounded above and below by positive constants for t ¥ (0, 1) and some fixed l > 0. This condition is independent of l. These results are proved by splitting any Gaussian semigroup (in a canonical way) into a semisimple part living on the commutator group GOE and an Abelian part living on A=G/GOE. For symmetric central Gaussian semigroups,

Author

A. Bendikov; L. Saloff-Coste

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-1236)

Published

2001

Language

EN

Field

Mathematics (Physical Sciences)