This paper discusses spectral synthesis for those modulation spaces Mp,qₛ( Rⁿ) 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-L\'evy theorem for Mp,qₛ( Rⁿ) and Fourier-Wermer algebras FLqₛ( Rⁿ).
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Feichtinger et al. (2024) studied this question.
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