Extended Sobolev scale on Zn

Abstract

In analogy with the definition of “extended Sobolev scale" on Rn by Mikhailets and Murach, working in the setting of the lattice Zn, we define the “extended Sobolev scale" Hφ(Zn), where φ is a function which is RO-varying at infinity. Using the scale Hφ(Zn), we describe all Hilbert function-spaces that serve as interpolation spaces with respect to a pair of discrete Sobolev spaces [H(s0)(Zn),H(s1)(Zn)], with s0