Optimal flat functions in Carleman-Roumieu ultraholomorphic classes in sectors

Abstract

We construct optimal flat functions in Carleman-Roumieu ultraholomorphic classes associated to general strongly nonquasianalytic weight sequences, and defined on sectors of suitably restricted opening. A general procedure is presented in order to obtain linear continuous extension operators, right inverses of the Borel map, for the case of regular weight sequences in the sense of Dyn'kin. Finally, we discuss some examples (including the well-known $q$-Gevrey case) where such optimal flat functions can be obtained in a more explicit way.

29 pages. Important improvements, mainly in Section 3: a simplified concept of optimal flat function is introduced, and their general construction is provided for strongly non-quasianalytic weight sequences and in narrow enough sectors

References in corpus (1)

• The Borel map in the mixed Beurling setting

Cited by in corpus (5)

• On the regularization of sequences and associated weight functions
• Ellipticity and the problem of iterates in Denjoy-Carleman classes
• Surjectivity of the asymptotic Borel map in Carleman ultraholomorphic classes defined by sequences with shifted moments
• On integral representations of $q$-difference operators and their applications
• On Orlicz classes defined in terms of associated weight functions