Fundamental Solutions to ?sub class="a-plus-plus"> b on Certain Quadrics

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• 作者：Albert Boggess ; Andrew Raich
• 关键词：Kohn Laplacian ; Complex Green operator ; Lie group ; Quadrics ; Heisenberg group ; Fundamental solution ; 32W10 ; 33C45 ; 43A80 ; 35H20
• 刊名：Journal of Geometric Analysis
• 出版年：2013
• 出版时间：October 2013
• 年：2013
• 卷：23
• 期：4
• 页码：1729-1752
• 全文大小：430KB
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• 作者单位：Albert Boggess (1)
  Andrew Raich (2)
  
  1. Department of Mathematics, Texas A&M University, Mailstop 3368, College Station, TX, 77845-3368, USA
  2. Department of Mathematical Sciences, 1 University of Arkansas, SCEN 327, Fayetteville, AR, 72701, USA
  
• ISSN：1559-002X

文摘

The purpose of this article is to expand the number of examples for which the complex Green operator, that is, the fundamental solution to the Kohn Laplacian, can be computed. We use the Lie group structure of quadric submanifolds of ?sup class="a-plus-plus"> n ×?sup class="a-plus-plus"> m and the group Fourier transform to reduce the ?sub class="a-plus-plus"> b equation to ones that can be solved using modified Hermite functions. We use Mehler’s formula and investigate (1)?quadric hypersurfaces, where the eigenvalues of the Levi form are not identical (including possibly zero eigenvalues), and (2)?the canonical quadrics in ?sup class="a-plus-plus">4 of codimension two.