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Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2018

Explicit formulas for {$C^{1,1}$} Glaeser-Whitney extensions of 1-fields in Hilbert spaces

Résumé

We give a simple alternative proof for the $C^{1,1}$--convex extension problem which has been introduced and studied by D. Azagra and C. Mudarra [2]. As an application, we obtain an easy constructive proof for the Glaeser-Whitney problem of $C^{1,1}$ extensions on a Hilbert space. In both cases we provide explicit formulae for the extensions. For the Gleaser-Whitney problem the obtained extension is almost minimal, that is, minimal up to a factor $\frac{1+\sqrt{3}}{2}$ in the sense of Le Gruyer [15].
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Dates et versions

hal-01530908 , version 1 (02-06-2017)
hal-01530908 , version 2 (17-02-2018)

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Citer

Aris Daniilidis, Mounir Haddou, Erwan Le Gruyer, Olivier Ley. Explicit formulas for {$C^{1,1}$} Glaeser-Whitney extensions of 1-fields in Hilbert spaces. Proceedings of the American Mathematical Society, 2018, 146 (10), pp.4487-4495. ⟨10.1090/proc/14012⟩. ⟨hal-01530908v2⟩
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