Density properties of Hankel translations of positive definite functions

Abstract.

In this paper we study density properties of the Hankel translations of certain positive definite (in the Hankel sense) functions on $(0,\infty )$. The density is understood in a Fréchet space of smooth functions on $(0,\infty )$ whose topology is defined by seminorms involving the Bessel operator $x^{-2\mu -1}Dx^{2\mu +1}D$.