On inclusion relations between weighted spaces of entire functions

TL;DR

This paper characterizes when weighted classes of entire functions are included within each other, using associated weights and sequences, and explores their stability under point-wise multiplication.

Contribution

It provides a comprehensive characterization of inclusion relations between weighted spaces of entire functions through associated weights and sequences.

Findings

Inclusion relations are characterized via associated weights and sequences.

Conditions for closedness under point-wise multiplication are established.

The framework reduces abstract weight functions to sequence-based settings.

Abstract

We characterize the inclusions of weighted classes of entire functions in terms of the defining weights resp. weight systems. First we treat weights defined in terms of a so-called associated weight function where the weight(system) is based on a given sequence. The abstract weight function case is then reduced to the weight sequence setting by using the so-called associated weight sequence. As an application of the main statements we characterize closedness under point-wise multiplication of these classes.