Hankel convolution on distribution spaces with exponential growth

A Generalized Hankel Convolution on Zemanian Spaces

We define a new generalized Hankel convolution on the Zemanian distribution spaces of slow growth.

Convolution and Homogeneous Spaces

Exponential Decomposition and Hankel Matrix

Calderón's reproducing formula for Hankel convolution

where φ :Rn → C and φt(x)= t−nφ(x/t), t > 0. For conditions of validity of identity (1.1), we may refer to [3]. Hankel convolution introduced by Hirschman Jr. [5] related to the Hankel transform was studied at length by Cholewinski [1] and Haimo [4]. Its distributional theory was developed byMarrero and Betancor [6]. Pathak and Pandey [8] used Hankel convolution in their study of pseudodifferen...

Exponential Growth of Spaces without Conjugate Points

An n-dimensional polyhedral space is a length space M (with intrinsic metric) triangulated into n-simplexes with smooth Riemannian metrics. In the definitions below, we assume that the triangulation is fixed. The boundary of M is the union of the (n− 1)-simplexes of the triangulation that are adjacent to only one (n− 1)-simplex. As usual, a geodesic in M is a naturally parametrized locally shor...