Further study of modulation spaces as Banach algebras

Abstract. This paper discusses spectral synthesis for those modulation spaces \(M^{p,q}_s({\mathbf R}^n)\) which form Banach algebras under pointwise multiplication. An important argument will be the ``ideal theory for Segal algebras'' by H. Reiter [15]. This paper is a continuation of our paper [5] where the case \(q=1\) is treated. As a by-product we obtain a variant of Wiener–Lévy theorem for \(M^{p,q}_s({\mathbf R}^n)\) and Fourier–Wermer algebras \({\mathcal F}L^q_s({\mathbf R}^n)\).