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An Elementary Symmetry-Based Derivation of the Heat Kernel on Heisenberg Group

Volume 14, Number 2 (2012), 82 - 89

An Elementary Symmetry-Based Derivation of the Heat Kernel on Heisenberg Group

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Abstract

Using symmetry arguments, we propose a simple derivation of a fundamental solution of the operator ∂t −ΔH in which ΔH is Kohn-Laplace operator on the Heisenberg group H2n+1. Our derivation extends that of Craddock and Lennox [J. Differential Equations 232(2007) 652-674]. Indeed, these authors solved the same problem by employing a symmetry approach in the case n = 1 . We demonstrate that the case n = 1 is quite peculiar from a symmetry standpoint and the extension of symmetry arguments to the case n > 1 requires some intermediate results.