, Volume 21, Issue 4, pp 803-818
Date: 21 Jun 2004

A Note on Hermite and Subelliptic Operators

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Abstract

In this note, we compute the fundamental solution for the Hermite operator with singularity at an arbitrary point y∈ℝ n . We also apply this result to obtain the fundamental solutions for the Grushin operator in ℝ2 and the sub-Laplacian in the Heisenberg group H n .

Dedicated to Professor Silei Wang on the occasion of his 70th brithday
The research is partially supported by a William Fulbright Research Grant and a Competitive Research Grant at Georgetown University