"On some properties of modulation spaces as Banach algebras"Kobayashi, MasaharuIn this talk, we give some properties of the modulation spaces $M_s^{p,1}({\mathbf R}^n)$ as commutative Banach algebras. In particular, we show the Wiener-L\'evy theorem for $M^{p,1}_s({\mathbf R}^n)$, and clarify the sets of spectral synthesis for $M^{p,1}_s ({\mathbf R}^n)$ by using the ``ideal theory for Segal algebras'' developed in Reiter. The inclusion relationship between the modulation space $M^{p,1}_0 ({\mathbf R})$ and the Fourier Segal algebra ${\mathcal F}A_p({\mathbf R})$ is also determined. This talk is based on joint works with Hans G. Feichtinger and Enji Sato. |
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