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- W2883822390 abstract "We give a simple alternative proof for the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C Superscript 1 comma 1> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:annotation encoding=application/x-tex>C^{1,1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>–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 <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C Superscript 1 comma 1> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:annotation encoding=application/x-tex>C^{1,1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> 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)." @default.
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- W2883822390 date "2018-07-13" @default.
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- W2883822390 title "Explicit formulas for 𝐶^{1,1} Glaeser-Whitney extensions of 1-Taylor fields in Hilbert spaces" @default.
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- W2883822390 doi "https://doi.org/10.1090/proc/14012" @default.
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