Submission date: 15 June 2023

Abstract:

We show that definable Whitney jets of class C^{m,ω}, where m is a nonnegative integer and ω is a modulus of continuity, are the restrictions of definable C^{m,ω}-functions; “definable” refers to an arbitrary given o-minimal expansion of the real field. This is true in a uniform way: any definable bounded family of Whitney jets of class C^{m,ω} extends to a definable bounded family of C^{m,ω}-functions. We also discuss a uniform C^m-version and how the extension depends on the modulus of continuity.

Mathematics Subject Classification:

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Full text arXiv 2306.09156: pdf, ps.