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Media type:
E-Book
Title:
The Sub-Laplacian operators of some model domains
Contains:
Frontmatter
Preface
Contents
1 Fourier analysis and Laplace operators on ℝn
2 The model domain, the sub-Laplacian operator and Cauchy–Szegö kernels
3 The fundamental solution for the operator Δλ: k = 1
4 Fundamental solution for the operator Δλ: k = 2 and n = 1
5 Fundamental solution for the operator Δ0: k = 2
6 Green’s function of the operator Δλ for general n and k
7 A geometric formula for the fundamental solution
Bibliography
Index
Published in:Advances in analysis and geometry ; volume 7
Extent:
1 Online-Ressource (XIV, 250 Seiten)
Language:
English
DOI:
10.1515/9783110642995
ISBN:
9783110642995;
9783110643176
Identifier:
Reproduction note:
Issued also in print
Origination:
Footnote:
In English
Description:
The book constructs explicitly the fundamental solution of the sub-Laplacian operator for a family of model domains in Cn+1. This type of domain is a good point-wise model for a Cauchy-Rieman (CR) manifold with diagonalizable Levi form. Qualitative results for such operators have been studied extensively, but exact formulas are difficult to derive. Exact formulas are closely related to the underlying geometry and lead to equations of classical types such as hypergeometric equations and Whittaker’s equations