On the equivalence between moderate growth-type conditions in the weight matrix setting
Abstract
We study the generalizations of the known equivalent reformulations of condition moderate growth from the single weight sequence to the weight matrix setting. This condition, also known in the literature under the name stability under ultradifferentiable operators, plays a significant role in the theory of ultradifferentiable (and ultraholomorophic) function classes defined in terms of weight sequences and its generalization becomes relevant when dealing with classes defined by weight matrices. In the matrix setting, we prove that the different mixed conditions are in general not equivalently satisfied anymore and we focus on weight matrices associated with (associated) weight functions.
Keywords
Cite
@article{arxiv.2106.14339,
title = {On the equivalence between moderate growth-type conditions in the weight matrix setting},
author = {Gerhard Schindl},
journal= {arXiv preprint arXiv:2106.14339},
year = {2022}
}
Comments
24 pages; small changes (misprints are corrected); this version has been accepted for publication in Note di Matematica