A Note on Hermite and Subelliptic Operators  

作　　者：Der Chen CHANG Jing Zhi TIE 

机构地区：[1]Department of Mathematics, Georgetown University, Washington, DC 20057-1233. USA [2]Department of Mathematics, University of Georgia, Athens, GA 30602-7403, USA

出　　处：《Acta Mathematica Sinica,English Series》2005年第4期803-818,共16页数学学报（英文版）

基　　金：partially supported by a William Fulbright Research Grant and a Competitive Research Grant at Georgetown University

摘　　要：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 R^2 and the sub-Laplacian in the Heisenberg group Hn.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 R^2 and the sub-Laplacian in the Heisenberg group Hn.

关 键 词：Hermite operator Heisenberg group SUB-LAPLACIAN Gruhsin operator Heat kernel Laguerre function 

分 类 号：O15[理学—数学]