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oai:uvadoc.uva.es:10324/490382025-02-17T14:08:03Zcom_10324_32197com_10324_952com_10324_894col_10324_32199

Surjectivity of the asymptotic borel map in Carleman–Roumieu ultraholomorphic classes defined by regular sequences Jimenez Garrido, Jesús Javier Sanz Gil, Javier Schindl, Gerhard 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, that was introduced by V. Thilliez. The techniques involve regular variation, integral transforms and characterization results of A. Debrouwere in a half-plane, stemming from his study of the surjectivity of the moment mapping in general Gelfand–Shilov spaces. 2021-10-13T11:05:04Z 2021-10-13T11:05:04Z 2021-10-13T11:05:04Z 2021 info:eu-repo/semantics/article Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2021, vol.115, n. 4, p. 1-18 1578-7303 https://uvadoc.uva.es/handle/10324/49038 10.1007/s13398-021-01119-y 4 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 115 1579-1505 eng https://link.springer.com/article/10.1007/s13398-021-01119-y info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/4.0/ © 2021 The Authors Atribución 4.0 Internacional Springer