Abstract
In this note, we compute the fundamental solution for the Hermite operator with singularity at an arbitrary point y∈ℝn. 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 .
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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
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Chang, D.C., Tie, J.Z. A Note on Hermite and Subelliptic Operators. Acta Math Sinica 21, 803–818 (2005). https://doi.org/10.1007/s10114-004-0336-0
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DOI: https://doi.org/10.1007/s10114-004-0336-0