Ultraholomorphic extension maps for spaces of ultradifferentiable jets
Institut de Mathématique, Université de Liège, Grande Traverse, 12, Sart Tilrnan Bat B 37, B-4000 LIEGE 1, BELGIUM, j.schmets@ulg.ac.be
Facultad de Matemáticas, Universidad de Valencia, Dr. Moliner 50, E-46100 BURJASOT (Valencia), SPAIN
Abstract
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