6533b86ffe1ef96bd12cdf4c
RESEARCH PRODUCT
On certain extension theorems in the mixed Borel setting
Jean SchmetsManuel Valdiviasubject
Discrete mathematicsBeurling typeApplied MathematicsUltradifferentiable functionsRoumieu typeHolomorphic functionMixed Borel theoremExtension (predicate logic)AnalysisMathematicsdescription
Abstract Given two sequences M 1 and M 2 of positive numbers, we give necessary and sufficient conditions under which the inclusions Λ { M 1 } ⊂ f (j) (0) j∈ N 0 : f∈ D { M 2 } [−1,1] , Λ ( M 1 ) ⊂ f (j) (0) j∈ N 0 : f∈ D ( M 2 ) [−1,1] hold, by means of explicit constructions. This answers a question raised by Chaumat and Chollet (Math. Ann. 298 (1994) 7–40). We also consider the case when [−1,1] is replaced by [−1,1]m as well as the possibility to get ultraholomorphic extensions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2004-09-01 | Journal of Mathematical Analysis and Applications |