Approximation rates for interpolation of Sobolev functions via Gaussians and allied functions

A Riesz-basis sequence for  L2[−π,π]L2[−π,π] is a strictly increasing sequence X:=(xj)j∈ZX:=(xj)j∈Z in RR such that the set of functions (e−ixj(⋅))j∈Z(e−ixj(⋅))j∈Z is a Riesz basis for L2[−π,π]L2[−π,π]. Given such a sequence and a parameter 0