1. CMB 2010 (vol 54 pp. 126)
|Fundamental Solutions of Kohn Sub-Laplacians on Anisotropic Heisenberg Groups and H-type Groups|
We prove that the fundamental solutions of Kohn sub-Laplacians $\Delta + i\alpha \partial_t$ on the anisotropic Heisenberg groups are tempered distributions and have meromorphic continuation in $\alpha$ with simple poles. We compute the residues and find the partial fundamental solutions at the poles. We also find formulas for the fundamental solutions for some matrix-valued Kohn type sub-Laplacians on H-type groups.
Categories:22E30, 35R03, 43A80
2. CMB 2007 (vol 50 pp. 291)
|Beurling's Theorem and Characterization of Heat Kernel for Riemannian Symmetric Spaces of Noncompact Type|
|Beurling's Theorem and Characterization of Heat Kernel for Riemannian Symmetric Spaces of Noncompact Type |
We prove Beurling's theorem for rank $1$ Riemannian symmetric spaces and relate its consequences with the characterization of the heat kernel of the symmetric space.
Keywords:Beurling's Theorem, Riemannian symmetric spaces, uncertainty principle
3. CMB 2002 (vol 45 pp. 364)
|Mellin Transforms of Whittaker Functions |
In this note we show that for an arbitrary reductive Lie group and any admissible irreducible Banach representation the Mellin transforms of Whittaker functions extend to meromorphic functions. We locate the possible poles and show that they always lie along translates of walls of Weyl chambers.
Categories:11F30, 22E30, 11F70, 22E45
4. CMB 2002 (vol 45 pp. 436)
|The Spherical Functions Related to the Root System $B_2$ |
In this paper, we give an integral formula for the eigenfunctions of the ring of differential operators related to the root system $B_2$.
Categories:43A90, 22E30, 33C80