Compatibility operators for degenerated elliptic equations on the ball and Heisenberg group
type: Item
instance of: scholarly article
title: Compatibility operators for degenerated elliptic equations on the ball and Heisenberg group
zbMATH Open document ID: 0538.47031
DOI: 10.1007/BF01161947
author: Robin C. Graham
published in: Mathematische Zeitschrift
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173491
review text: Differential operators on the Heisenberg group and odd dimensional spheres are derived whose smooth solutions are exactly the boundary values of smooth solutions of certain degenerate elliptic operators generalizing the Laplace-Beltrami operator in the Bergman metric on the Siegel domain or the complex ball. On the Heisenberg group these ''compatibility operators'' are products of Folland-Stein \({\mathcal L}_{\alpha}\) operators. A transformation law for these operators under the Cayley transform is derived as well as explicit formulae for their fundamental solutions.
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 58J32
zbMATH DE Number: 3855821
zbMATH Keywords: degenerate elliptic equations
zbMATH Keywords: Heisenberg group
zbMATH Keywords: elliptic operators generalizing the Laplace-Beltrami operator in the Bergman metric on the Siegel domain
zbMATH Keywords: compatibility operators
zbMATH Keywords: transformation law
zbMATH Keywords: Cayley transform
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3855821