Solid hulls and cores of classes of weighted entire functions defined in terms of associated weight functions

Abstract

In the spirit of very recent articles by J. Bonet, W. Lusky and J. Taskinen we are studying the so-called solid hulls and cores of spaces of weighted entire functions when the weights are given in terms of associated weight functions coming from weight sequences. These sequences are required to satisfy certain (standard) growth and regularity properties which are frequently arising and used in the theory of ultradifferentiable and ultraholomorphic function classes (where also the associated weight function plays a prominent role). Thanks to this additional information we are able to see which growth behavior the so-called ”Lusky-numbers”, arising in the representations of the solid hulls and cores, have to satisfy resp. if such numbers can exist.