On some properties of modulation spaces as Banach algebras

2024/05/15 by Feichtinger, Hans G., Kobayashi, Masaharu, Sato, Enji · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2405.09058

Abstract

In this paper, we give some properties of the modulation spaces M_s^p,1(\mathbf Rⁿ) as commutative Banach algebras. In particular, we show the Wiener-Lévy theorem for M^p,1_s(\mathbf Rⁿ), and clarify the sets of spectral synthesis for M^p,1_s (\mathbf Rⁿ) by using the ``ideal theory for Segal algebras'' developed in Reiter [30].The inclusion relationship between the modulation space M^p,1₀ (\mathbf R) and the Fourier Segal algebra \mathcal F\hspace-0.08cmA_p(\mathbf R) is also determined.

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