The surjectivity of the Borel mapping in the mixed setting for ultradifferentiable ramification spaces

Abstract

We consider r-ramification ultradifferentiable classes, introduced by J. Schmets and M. Valdivia in order to study the surjectivity of the Borel map, and later on also exploited by the authors in the ultraholomorphic context. We characterize quasianalyticity in such classes, extend the results of Schmets and Valdivia about the image of the Borel map in a mixed ultradifferentiable setting, and obtain a version of the Whitney extension theorem in this framework.

31 pages; this version has been accepted for publication in Monatsh. Math

References in corpus (3)

• Injectivity and surjectivity of the asymptotic Borel map in Carleman ultraholomorphic classes
• Indices of O-regular variation for weight functions and weight sequences
• On the extension of Whitney ultrajets, II

Cited by in corpus (9)

• Equality of ultradifferentiable classes by means of indices of mixed O-regular variation
• Ultraholomorphic extension theorems in the mixed setting
• On the inclusion relations of global ultradifferentiable classes defined by weight matrices
• On the maximal extension in the mixed ultradifferentiable weight sequence setting
• The Borel map in the mixed Beurling setting
• On optimal solutions of the Borel problem in the Roumieu case
• Solid hulls and cores of classes of weighted entire functions defined in terms of associated weight functions
• Ultraholomorphic sectorial extensions of Beurling type
• Construction of the log-convex minorant of a sequence $\{M_{\alpha }{\}}_{\alpha \in {\mathbb{N}}_0^d}$