Solvable extensions of H-type groups provide a unified approach to noncompact symmetric spaces of rank one. In this paper we prove optimal pointwise estimates for the heat kernel for complex time p_z. We deduce sharp L^p estimates both for p_z and for the complex heat kernel corresponding to a distinguished right-invariant Laplacian, associated to the Laplace Beltrami operator.
Heat Kernel Bounds for Complex Time on Hyperbolic Spaces and Solvable Extensions of H-type Groups
GIULINI, SAVERIO;
1997-01-01
Abstract
Solvable extensions of H-type groups provide a unified approach to noncompact symmetric spaces of rank one. In this paper we prove optimal pointwise estimates for the heat kernel for complex time p_z. We deduce sharp L^p estimates both for p_z and for the complex heat kernel corresponding to a distinguished right-invariant Laplacian, associated to the Laplace Beltrami operator.
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