Gohberg-Krupnik Localisation for Discrete Wiener-Hopf Operators on Orlicz Sequence Spaces

Let $Φ$ be an N-function whose Matuszewska-Orlicz indices satisfy 1<α_Φ≤β_Φ<∞. Using these indices, we introduce ``interpolation friendly" classes of Fourier multipliers M[Φ] and MΦ such that M[Φ]⊂ MΦ⊂ M_Φ, where M_Φ is the Banach algebra of all Fourier multipliers on the reflexive Orlicz sequence space ^Φ(Z). Applying the Gohberg-Krupnik localisation in the corresponding Calkin algebra, the study of Fredholmness of the discrete Wiener-Hopf operator $T(a)$ with a∈ MΦ is reduced to that of T(a_τ) for certain, potentially easier to study, local representatives a_τ∈ M[Φ] of a at all points τ∈[-π,π).