Spectral density on the quaternionic Heisenberg group and a Green kernel for fractional powers of its Casimir-Laplacian

Abstract

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 [14] and then find its spectral density. Also we obtain the Green kernel for fractional powers of the Casimir-Laplace operator.

Keywords

• Quaternionic Heisenberg group
• Casimir-Laplacian
• resolvent kernel
• spectral density
• Green function
• Whittaker function
• generalized Laguerre polynomials