A Pe{\l}czy\'nski-Vogt decomposition result for (PLS)-spaces and sequence space representations

TL;DR

This paper proves a Pelczynski-Vogt decomposition for (PLS)-type power series spaces and uses it with Gabor frame theory to represent multiplier spaces of Gelfand-Shilov spaces, advancing the understanding of their structure.

Contribution

It introduces a Pelczynski-Vogt decomposition for (PLS)-spaces and applies it to derive sequence space representations for multiplier spaces of Gelfand-Shilov spaces.

Findings

Decomposition result for (PLS)-spaces established

Sequence space representations for multiplier spaces derived

Enhanced understanding of Gelfand-Shilov space multipliers

Abstract

We establish a Pelczy\'nski-Vogt decomposition result for (PLS)-type power series spaces of infinite type. By combining this result with the theory of Gabor frames, we obtain sequence space representations for multiplier spaces of Gelfand-Shilov spaces of Beurling type.