Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 39, pp. 1-11.

Title: Resolvent kernel on H-type groups and a Green kernel for fractional powers of its sub-Laplacian
       
Author: Zakariyae Mouhcine (Univ. S. M. Ben Abdellah, Fez, Morocco)

Abstract:    
In this article, we give an integral representation of the resolvent kernel on H-type groups,
then we derive an integral representation of Kaplan's fundamental solution on this groups.
Also we obtain the Green kernel for fractional powers of its sub-Laplacian.

Submitted December 7, 2021. Published May 19, 2022.
Math Subject Classifications: 22E25, 22E30, 35K08.
Key Words: H-type groups; sub-Laplacian; resolvent kernel; Green kernel; Whittaker function.