Wiener amalgam spaces of quasianalytic ultradistributions

TL;DR

This paper introduces Wiener amalgam spaces for quasianalytic ultradistributions, characterizing their structure, duals, and interpolation properties within a broad functional analysis framework.

Contribution

It defines new Wiener amalgam spaces for quasianalytic ultradistributions with detailed characterizations and duality results, expanding the functional analysis toolkit.

Findings

Discrete characterization via uniformly concentrated partitions of unity.

Identification of strong duals for most Wiener amalgam spaces.

Analysis of complex interpolation properties.

Abstract

We define Wiener amalgam spaces of (quasi)analytic ultradistributions whose local components belong to a general class of translation and modulation invariant Banach spaces of ultradistributions and their global components are either weighted $L^p$ or weighted $\mathcal{C}_0$ spaces. We provide a discrete characterisation via so called uniformly concentrated partitions of unity. Finally, we study the complex interpolation method and we identify the strong duals for most of these Wiener amalgam spaces.