Fundamental Solutions to □b on Certain Quadrics

Albert Boggess, Andrew Raich

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

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 Lapla-cian, can be computed. We use the Lie group structure of quadric submanifolds of ℂn × ℂm and the group Fourier transform to reduce the □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 ℂ4of codimension two.

Original languageEnglish (US)
Pages (from-to)1729-1752
Number of pages24
JournalJournal of Geometric Analysis
Volume23
Issue number4
DOIs
StatePublished - Jan 1 2013
Externally publishedYes

Keywords

  • Complex Green operator
  • Fundamental solution
  • Heisenberg group
  • Kohn Laplacian
  • Lie group
  • Quadrics

ASJC Scopus subject areas

  • Geometry and Topology

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