On optimal solutions of the Borel problem in the Roumieu case
Copyright policy )On optimal solutions of the Borel problem in the Roumieu case
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.
18 pages; minor changes, Remark 4.7 added
- University of Vienna Austria
ultradifferentiable function classes, Borel map, Mathematics - Complex Variables, 101002 Analysis, Spaces defined by inductive or projective limits (LB, LF, etc.), controlled loss of regularity, Rings and algebras of continuous, differentiable or analytic functions, Functional Analysis (math.FA), mixed setting, Mathematics - Functional Analysis, extension results, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, \(C^\infty\)-functions, quasi-analytic functions, Topological linear spaces of continuous, differentiable or analytic functions, Complex Variables (math.CV)
ultradifferentiable function classes, Borel map, Mathematics - Complex Variables, 101002 Analysis, Spaces defined by inductive or projective limits (LB, LF, etc.), controlled loss of regularity, Rings and algebras of continuous, differentiable or analytic functions, Functional Analysis (math.FA), mixed setting, Mathematics - Functional Analysis, extension results, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, \(C^\infty\)-functions, quasi-analytic functions, Topological linear spaces of continuous, differentiable or analytic functions, Complex Variables (math.CV)
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