Gelfand-Shilov spaces for the Hankel transform

AbstractWe introduce the subspaces Ga, Gβ and Gβa(a, β⩾0) of the Schwartz space S+ defined on the interval (0, + ∞), which are associated with the Hankel transform in the same way as the Gelfand-Shilov spaces Sa, Sβ and Sβa are with the Fourier transform. That is, the Hankel transform defined as Hyf(x)=12∫0∞f(t)(tx)-(y/2)tyJy(xt)dt (y>-1) is an isomorphism from Ga, Gβ and Gβa onto Ga, Gβ and Gaβ. We exten d this result for the fractional powers of the Hankel transform and for modified fractional powers of the Hankel transform