In this article, we introduce a new integral representation of the resolvent kernel for the Casimir-Laplacian on the quaternionic Heisenberg group which was obtained in  and then find its spectral density. Also we obtain the Green kernel for fractional powers of the Casimir-Laplace operator.
Submitted February 6, 2017. Published March 4, 2017.
Math Subject Classifications: 22E30, 47B34, 47A10, 35P05.
Key Words: Quaternionic Heisenberg group; Casimir-Laplacian; resolvent kernel; spectral density; Green function; Whittaker function; generalized Laguerre polynomials.
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| Zakariyae Mouhcine |
PDE and Spectral Geometry, Laboratory of Analysis and Applications - URAC/03
Department of Mathematics, Faculty of Sciences,
Mohammed V University in Rabat
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