The Sub-Laplacian Operators of Some Model Domains / / Jingzhi Tie, Der-Chen Chang.

• Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2022 Part 1
• VerfasserIn: Chang, Der-Chen,; Tie, Jingzhi,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2022]; ©2022
• Year of Publication: 2022
• Language: English
• Series: Advances in Analysis and Geometry , 7
• Physical Description: 1 online resource (XIV, 252 p.)

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.

Table of Contents

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