On some properties of modulation spaces as Banach algebras
Studia Mathematica
MSC: Primary 42B35; Secondary 43A45
DOI: 10.4064/sm240316-9-9
Published online: 13 December 2024
Abstract
We give some properties of the modulation spaces $M_s^{p,1}(\mathbf R^n)$ as commutative Banach algebras. In particular, we prove the Wiener–Lévy 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 by Reiter. The inclusion relationship between the modulation space $M^{p,1}_0 (\mathbf R)$ and the Fourier Segal algebra $\mathcal FA_p(\mathbf R)$ is also determined.
