On optimal solutions of the Borel problem in the Roumieu case

Abstract

The Borel problem for Denjoy--Carleman and Braun--Meise--Taylor classes has well-known optimal solutions. The unified treatment of these ultradifferentiable classes by means of one-parameter families of weight sequences allows to compare these optimal solutions. We determine the relations among them and give conditions for their equivalence in the Roumieu case.

arXiv comment18 pages; minor changes, Remark 4.7 added

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Cited by in corpus (2)

• On generalized definitions of ultradifferentiable classes
• On inclusion relations of weighted $L^p$-type spaces defined in terms of weight function matrices