A Weighted Version of Wiener’s Lemma in p-normed Algebras for 0 < p ≤ 1

Abstract

In this paper we give a generalization of Wiener’s lemma. We show that the pointwise inverse of a non-vanishining GRS-weighted absolutely convergent d-dimensional Fourier series in the p-normed algebra $\mathcal{A}_{p}^{v}(\mathbb{T}^{d})\;\mathrm{for}\; 0<\;p\;\leq 1$, is also a GRS-weighted absolutely convergent Fourier series in $\mathcal{A}_{p}^{v}(\mathbb{T}^{d})$This extends the previously known result in the case d = 1.

Mathematics Subject Classification (2010). 43, 46.