On strong growth conditions for weighted spaces of entire functions
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.
Keywords
Cite
@article{arxiv.2401.14330,
title = {On strong growth conditions for weighted spaces of entire functions},
author = {Gerhard Schindl},
journal= {arXiv preprint arXiv:2401.14330},
year = {2024}
}
Comments
30 pages; this is the second part of the first version of submission arXiv:2211.14374. The proofs of Prop. 4.7 & 4.12, and hence of Cor. 4.14, in the first part contain a technical gap; in the appendix of this paper we provide a correction. Some stylistic changes according to the suggestions by the anonymous referee have been applied; this version is published in Bull. Sci. math