2025/09/14 by Oleksiy Karlovych, Karlovych, Oleksiy, Sandra Mary Thampi +1
Mathematics · #Mathematical Analysis and Transform Methods #Holomorphic and Operator Theory #Algebraic and Geometric Analysis
paper · pdf · doi:10.48550/arxiv.2509.11203
Let Φ be an N-function whose Matuszewska-Orlicz indices satisfy 1<αΦ≤βΦ<∞. Using these indices, we introduce ``interpolation friendly" classes of Fourier multipliers M[Φ] and M⟨Φ⟩ such that M[Φ]⊂ M⟨Φ⟩⊂ MΦ, where MΦ is the Banach algebra of all Fourier multipliers on the reflexive Orlicz sequence space ℓΦ(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∈ M⟨Φ⟩ is reduced to that of T(aτ) for certain, potentially easier to study, local representatives aτ∈ M[Φ] of a at all points τ∈[-π,π).