Translation-modulation invariant Banach spaces of ultradistributions

Abstract

We introduce and study a new class of translation-modulation invariant Banach spaces of ultradistributions. These spaces show stability under Fourier transform and tensor products; furthermore, they have a natural Banach convolution module structure over a certain associated Beurling algebra, as well as a Banach multiplication module structure over an associated Wiener-Beurling algebra. We also investigate a new class of modulation spaces, the Banach spaces of ultradistributions ${\mathcal{M}}^F$ on ${\mathbb{R}}^d$, associated to translation-modulation invariant Banach spaces of ultradistributions $F$ on ${\mathbb{R}}^{2d}$.

arXiv comment19 pages

References in corpus (4)

• New distribution spaces associated to translation-invariant Banach spaces
• On quasianalytic classes of Gelfand-Shilov type. Parametrix and convolution
• Convolution of ultradistributions and ultradistribution spaces associated to translation-invariant Banach spaces
• Boundary values of holomorphic functions and heat kernel method in translation-invariant distribution spaces

Cited by in corpus (3)

• Modulation spaces associated to tensor products of amalgam spaces
• Convolutors of translation-modulation invariant Banach spaces of ultradistributions
• Sequence space representations for translation-modulation invariant function and distribution spaces