Translation-modulation invariant Banach spaces of ultradistributions

Dimovski, Pavel; Pilipovic, Stevan; Prangoski, Bojan; Vindas, Jasson

doi:https://doi.org/10.1007/s00041-018-9610-x

Translation-modulation invariant Banach spaces of ultradistributions

Journal

Journal of Fourier Analysis and Applications

Date Issued

2018-04-30

Author(s)

Dimovski, Pavel

Pilipovic, Stevan

Vindas, Jasson

DOI

https://doi.org/10.1007/s00041-018-9610-x

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 MF on Rd , associated to translation–modulation invariant Banach spaces of ultradistributions F on R2d .