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 extens...

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