Mouhcine, Zakariyae2022-04-012022-04-012017-03-04Mouhcine, Z. (2017). Spectral density on the quaternionic Heisenberg group and a Green kernel for fractional powers of its Casimir-Laplacian. <i>Electronic Journal of Differential Equations, 2017</i>(64), pp. 1-12.1072-6691https://hdl.handle.net/10877/15590In 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.Text12 pages1 file (.pdf)enAttribution 4.0 InternationalQuaternionic Heisenberg groupCasimir-LaplacianResolvent kernelSpectral densityGreen functionWhittaker functionGeneralized Laguerre polynomialsArticle