A new characterization of the bounded operators commuting with Hankel translation

Abstract.

In this note we prove that a bounded operator in the Zemanian space ${\cal H}_\mu$ commutes with the Hankel translation if, and only if, it commutes with the Bessel operator $S_\mu = x^ {-\mu -1/2}Dx^ {2\mu +1}Dx^ {-\mu -1/2}$.