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Ultraholomorphic extension maps for spaces of ultradifferentiable jets

(Volume 70 - Année 2001 — Numéro 4 - 5 - 6)
Open Access
Mots-clés : Whiney jet, extension map, real-analytic extention, ultradifferentiable jet/function, ultraholomorphic function, Beurling type, Roumieu type


The key results provide ultraholomorphic approximation continuous linear maps for spaces of ultradifferentiable functions on an open subset of n. They lead to results about the existence of continuous linear extension maps from the spaces of the ultradifferentiable Whitney jets of Beurling or Roumieu type on a closed subset F of n. Their values belong to spaces of functions defined on n  D : they are ultradifferentiable on n and ultraholomorphic on D, an open subset of n such that D  n = n F. We consider the cases when the ultradifferentiable jets and functions are defined by means of a weight or of a sequence of positive numbers.

1Mathematics Subject Classification: Primary: 46E10, 30D60, 32D99

2Secondary: 46A13, 30H05, 26E05

To cite this article

Jean SCHMETS & Manuel VALDIVIA, «Ultraholomorphic extension maps for spaces of ultradifferentiable jets», Bulletin de la Société Royale des Sciences de Liège [En ligne], Numéro 4 - 5 - 6, Volume 70 - Année 2001, 373 – 394 URL :

About: Jean SCHMETS

Institut de Mathématique, Université de Liège, Grande Traverse, 12, Sart Tilrnan Bat B 37, B-4000 LIEGE 1, BELGIUM,

About: Manuel VALDIVIA

Facultad de Matemáticas, Universidad de Valencia, Dr. Moliner 50, E-46100 BURJASOT (Valencia), SPAIN