On inclusion relations between weighted spaces of entire functions

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.

38 pages; this version is published in Bull. Sci. Math. The first submission has been split into two parts: The first one is this recent version; the second part "On strong growth conditions for weighted spaces of entire functions" contains in the appendix corrections of the gap in the proofs of Prop. 4.7 & 4.12, and Cor. 4.14

References in corpus (2)

• On generalized definitions of ultradifferentiable classes
• Ultradifferentiable classes of entire functions

Cited by in corpus (5)

• On the regularization of sequences and associated weight functions
• On strong growth conditions for weighted spaces of entire functions
• On inclusion relations of weighted $L^p$-type spaces defined in terms of weight function matrices
• On the conjugate weight function and ultradifferentiable classes of entire functions
• On Orlicz classes defined in terms of associated weight functions