On the extension of Whitney ultrajets

Abstract

We prove necessary and sufficient conditions for the validity of Whitney's extension theorem in the ultradifferentiable Roumieu setting with controlled loss of regularity.

27 pages; some minor changes, accepted for publication in Studia Mathematica

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• Sectorial extensions, via Laplace transforms, in ultraholomorphic classes defined by weight functions
• The Theorem of Iterates for elliptic and non-elliptic Operators
• The surjectivity of the Borel mapping in the mixed setting for ultradifferentiable ramification spaces
• Ultradifferentiable extension theorems: a survey
• Nonlinear conditions for ultradifferentiability
• The Borel map in the mixed Beurling setting
• Ultraholomorphic sectorial extensions of Beurling type
• Nonlinear conditions for ultradifferentiability: a uniform approach