On the equivalence between moderate growth-type conditions in the weight matrix setting


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.

DOI Code: 10.1285/i15900932v42n1p1

Keywords: Weight sequences; weight functions and weight matrices; classes of ultradifferentiable functions; moderate growth; growth and regularity properties for sequences

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