Continuously Differentiable Functions on Compact Sets

Loosveldt, Laurent; Wengenroth, Jochen; Frerick, Leonhard

doi:10.1007/s00025-020-01303-3

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Continuously Differentiable Functions on Compact Sets

Loosveldt, Laurent; Wengenroth, Jochen; Frerick, Leonhard

2020 • In Results in Mathematics, 75 (4)

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https://hdl.handle.net/2268/252060

DOI
10.1007/s00025-020-01303-3

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Keywords :

Differentiability on compact sets; Whitney jets

Abstract :

[en] We consider the space C^1(K) of real-valued continuously differentiable functions on a compact set K ⊆ Rd. We characterize the completeness of this space and prove that the restriction space C^1(Rd|K) ={f|K : f ∈ C1(Rd)} is always dense in C1(K). The space C1(K) is then compared with other spaces of differentiable functions on compact sets.

Disciplines :

Mathematics

Author, co-author :

Loosveldt, Laurent ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes

Wengenroth, Jochen; Université de Trèves - Universität Trier

Frerick, Leonhard; Université de Trèves - Universität Trier

Language :

English

Title :

Continuously Differentiable Functions on Compact Sets

Alternative titles :

[en] Fonctions continument dérivables sur

Publication date :

December 2020

Journal title :

Results in Mathematics

ISSN :

1422-6383

eISSN :

1420-9012

Publisher :

Springer, Germany

Volume :

Issue :

Peer reviewed :

Peer Reviewed verified by ORBi

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
ULiège - Université de Liège [BE]
UniGR - Université de la Grande Région [LU]

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since 28 October 2020

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Bibliography

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