Surjectivity of the asymptotic Borel map in Carleman-Roumieu ultraholomorphic classes defined by regular sequences
arXiv:2007.06310 · doi:10.1007/s13398-021-01119-y
Abstract
We study the surjectivity of, and the existence of right inverses for, the asymptotic Borel map in Carleman-Roumieu ultraholomorphic classes defined by regular sequences in the sense of E. M. Dyn'kin. We extend previous results by J. Schmets and M. Valdivia, by V. Thilliez, and by the authors, and show the prominent role played by an index associated with the sequence and introduced by Thilliez. The techniques involve regular variation, integral transforms and characterization results of A. Debrouwere in a half-plane, steming from his study of the surjectivity of the moment mapping in general Gelfand-Shilov spaces.
18 pages. Some changes are related to an index shift in condition , property (9) and the proof of Proposition 4.4. The example proving that (vii) does not imply (vi) in that Proposition has been changed. New proof, avoiding the use of condition (dc), for the implication from (i) to (ii) in Theorem 4.5. Some new comments added and some misprints corrected