On strong growth conditions for weighted spaces of entire functions

TL;DR

This paper characterizes inclusion relations and growth comparisons between weighted classes of entire functions, focusing on associated weight functions and sequences, and comparing different weight systems.

Contribution

It introduces new characterizations of inclusion and growth relations for weighted entire function spaces using associated weight functions and sequences.

Findings

Established criteria for inclusion relations between weighted classes

Compared dilatation-type and exponential-type weight systems

Reduced abstract weight function analysis to weight sequence setting

Abstract

We characterize the inclusion relations between weighted classes of entire functions with rapid decreasing growth and study strong growth comparison relations between given weights. In our considerations first we focus on weights defined in terms of the so-called associated weight function where the weight(system) is based on a given sequence. Then the abstract weight function case is reduced to the weight sequence setting by using the so-called associated weight sequence. Finally, we compare weighted entire function spaces defined in terms of so-called dilatation-type and exponential-type weight systems.