On the inclusion relations of global ultradifferentiable classes defined by weight matrices

Abstract

We study and characterize the inclusion relations of global classes in the general weight matrix framework in terms of growth relations for the defining weight matrices. We consider the Roumieu and Beurling cases, and as a particular case we also treat the classical weight function and weight sequence cases. Moreover, we construct a weight sequence which is oscillating around any weight sequence which satisfies some minimal conditions and, in particular, around the critical weight sequence $(p!{)}^{1/2}$, related with the non-triviality of the classes. Finally, we also obtain comparison results both on classes defined by weight functions that can be defined by weight sequences and conversely.

References in corpus (5)

• Composition in ultradifferentiable classes
• Almost analytic extensions of ultradifferentiable functions with applications to microlocal analysis
• Extension of Whitney jets of controlled growth
• The Theorem of Iterates for elliptic and non-elliptic Operators
• The surjectivity of the Borel mapping in the mixed setting for ultradifferentiable ramification spaces

Cited by in corpus (3)

• On the regularization of sequences and associated weight functions
• Gelfand-Shilov spaces for extended Gevrey regularity
• Construction of the log-convex minorant of a sequence $\{M_{\alpha }{\}}_{\alpha \in {\mathbb{N}}_0^d}$