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.
Author(s): Jingzhi Tie, Der-Chen Chang
Series: Advances in Analysis and Geometry, 7
Publisher: De Gruyter
Year: 2022
Language: English
Pages: 265
City: Berlin
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
