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

Daniilidis, Aris; Haddou, Mounir; Le Gruyer, Erwan; Ley, Olivier

doi:10.1090/proc/14012

Explicit formulas for $C^{1,1}$ Glaeser-Whitney extensions of $1$-Taylor fields in Hilbert spaces
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by Aris Daniilidis, Mounir Haddou, Erwan Le Gruyer and Olivier Ley

Proc. Amer. Math. Soc. 146 (2018), 4487-4495

DOI: https://doi.org/10.1090/proc/14012

Published electronically: July 13, 2018

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Abstract:

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 (2017). 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 Glaeser-Whitney problem the obtained extension is almost minimal, that is, minimal up to a multiplicative factor in the sense of Le Gruyer (2009).

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