Further study of modulation spaces as Banach algebras

Abstract

This paper discusses spectral synthesis for those modulation spaces $M_s^{p,q}({\mathbf{R}}^n)$ 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 $M_s^{p,q}({\mathbf{R}}^n)$ and Fourier-Wermer algebras $\mathcal{F}{L}_s^q({\mathbf{R}}^n)$.