On certain extension theorems in the mixed Borel setting

Given two sequencesM1 andM2 of positive numbers, we give necessary and sufficient conditions under which the inclusions Λ{M1} ⊂ f (j )(0) j∈N0 : f ∈ D{M2} [−1, 1] , Λ(M1) ⊂ f (j )(0) j∈N0 : f ∈ D(M2) [−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.  2003 Elsevier Inc. All rights reserved