On the meromorphic continuation of the Mellin transform associated to the wave kernel on Riemannian symmetric spaces of the non-compact type

Abstract

We considered the Mellin transform assigned to the convolution wave kernel associated to the Laplace-Beltrami operator on higher rank Riemannian symmetric spaces of the non-compact type. The occurrence of the analyticity strip of this transform can be deduced directly from the pointwise kernel estimates. Using the zeta function techniques, we established its meromorphic extension to the entire complex plane $ {{\Bbb C}} $ with simple poles on the real line.

Keywords

• riemannian symmetric spaces
• wave kernel
• mellin transform
• asymptotic expansion
• meromorphic continuation
• zeta function