Details

Autor(en) / Beteiligte

• Frerick, Leonhard
• Loosveldt, Laurent
• Wengenroth, Jochen

Titel

Continuously Differentiable Functions on Compact Sets

Ist Teil von

• Resultate der Mathematik, 2020-12, Vol.75 (4), Article 177

Ort / Verlag

Cham: Springer International Publishing

Erscheinungsjahr

2020

Quelle

SpringerLink

Beschreibungen/Notizen

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