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 language | English (US) |
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Pages (from-to) | 1729-1752 |
Number of pages | 24 |
Journal | Journal of Geometric Analysis |
Volume | 23 |
Issue number | 4 |
DOIs | |
State | Published - Oct 2013 |
Externally published | Yes |
Keywords
- Complex Green operator
- Fundamental solution
- Heisenberg group
- Kohn Laplacian
- Lie group
- Quadrics
ASJC Scopus subject areas
- Geometry and Topology