The Paneitz operator on the anisotropic quaternionic Heisenberg group. Issue 11 (2nd November 2021)

• Record Type: Journal Article
• Authors: Wang, Haimeng; Chen, Bo
• Is Part Of: Complex variables and elliptic equations. Volume 66:Issue 11(2021)
• Page Start: 1941
• Page End: 1958
• Publication Date: 2021-11-02
• Subjects: Fundamental solution -- group Fourier transform -- Paneitz operator -- the anisotropic quaternionic Heisenberg group; 35A08 -- 35H20; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2020.1807963
• Languages: English
• ISSNs: 1747-6933

Abstract

ABSTRACT: We use the representation theory of nilpotent Lie groups of step two to find the fundamental solution for the Paneitz operator on the anisotropic quaternionic Heisenberg group. For the isotropic case, we also construct the closed-form of this solution. This result is the extension of the conclusion on the Heisenberg group.