On generalized definitions of ultradifferentiable classes
Javier Jiménez-Garrido, David Nicolas Nenning, Gerhard Schindl
Abstract
We show that the ultradifferentiable-like classes of smooth functions introduced and studied by S. Pilipović, N. Teofanov and F. Tomić are special cases of the general framework of spaces of ultradifferentiable functions defined in terms of weight matrices in the sense of A. Rainer and the third author. We study classes “beyond geometric growth factors” defined in terms of a weight sequence and an exponent sequence, prove that these new types admit a weight matrix representation and transfer known results from the matrix-type to such a non-standard ultradifferentiable setting.
Topics & Concepts
MathematicsSequence (biology)Representation (politics)ExponentMatrix (chemical analysis)Pure mathematicsType (biology)Transfer (computing)CombinatoricsChemistryComputer sciencePhilosophyParallel computingLinguisticsChromatographyEcologyPolitical sciencePoliticsBiologyBiochemistryLawMathematical Analysis and Transform MethodsAdvanced Harmonic Analysis ResearchAdvanced Banach Space Theory