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arXiv · 2405.09060

Further study of modulation spaces as Banach algebras

Hans G. Feichtinger·Masaharu Kobayashi·Enji Sato
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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-L\'evy theorem for $M^{p,q}_s({\mathbf R}^n)$ and Fourier-Wermer algebras ${\mathcal F}L^q_s({\mathbf R}^n)$.

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Hans G. Feichtinger, Masaharu Kobayashi, Enji Sato. 2024-05-15. Further study of modulation spaces as Banach algebras. https://arxiv.org/abs/2405.09060

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