Electron. J. Differential Equations, Vol. 2022 (2022), No. 39, pp. 1-11.

Resolvent kernel on H-type groups and a Green kernel for fractional powers of its sub-Laplacian

Zakariyae Mouhcine

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.

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Zakariyae Mouhcine
Laboratory of Modeling and Mathematical Structures
Department of Mathematics
Faculty of Science and Technology of Fez, Box 2202
University S. M. Ben Abdellah
Fez, Morocco
email: zakariyaemouhcine@gmail.com

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