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- Title
An explicit formula for the heat kernel of a left invariant operator.
- Authors
Urban, Roman
- Abstract
The main aim of this note is to find an explicit integral formula for the heat kernel of a certain second-order left invariant differential operator on a solvable Lie group, being a semi-direct product ℝ x ℝ, by means of a skew-product formula for diffusions. An explicit formula of a different kind for the special case of the operator considered in this note (the operator without the drift term) was found recently by Calin, Chang and Li. As a corollary from our main result we get a simple formula for the return probability from which the asymptotic behaviour for small and large values of time follows easily.
- Subjects
DIFFERENTIAL operators; DIFFERENTIAL equations; ASYMPTOTIC distribution; LIE groups; HEAT equation
- Publication
ALEA. Latin American Journal of Probability & Mathematical Statistics, 2014, Vol 11, p299
- ISSN
1980-0436
- Publication type
Article