Acta Mathematica Sinica

, Volume 21, Issue 4, pp 803–818

A Note on Hermite and Subelliptic Operators

ORIGINAL ARTICLES

DOI: 10.1007/s10114-004-0336-0

Cite this article as:
Chang, D.C. & Tie, J.Z. Acta Math Sinica (2005) 21: 803. doi:10.1007/s10114-004-0336-0

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 Hn.

Keywords

Hermite operator  Heisenberg group Sub-Laplacian Gruhsin operator Heat kernel Laguerre function 

MR (2000) Subject Classification

35A08 42B20 

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsGeorgetown UniversityWashingtonUSA
  2. 2.Department of MathematicsUniversity of GeorgiaAthensUSA

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