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.

arXiv comment30 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

References in corpus (6)

• Composition in ultradifferentiable classes
• Moduli of holomorphic functions and logarithmically convex radial weights
• On generalized definitions of ultradifferentiable classes
• On the regularization of sequences and associated weight functions
• On inclusion relations between weighted spaces of entire functions
• On the construction of large Algebras not contained in the image of the Borel map

Cited by in corpus (2)

• On the regularization of sequences and associated weight functions
• On inclusion relations of weighted $L^p$-type spaces defined in terms of weight function matrices