Abstract
AbstractWe consider the space $$C^1(K)$$
C
1
(
K
)
of real-valued continuously differentiable functions on a compact set $$K\subseteq \mathbb {R}^d$$
K
⊆
R
d
. We characterize the completeness of this space and prove that the restriction space $$C^1(\mathbb {R}^d|K)=\{f|_K: f\in C^1(\mathbb {R}^d)\}$$
C
1
(
R
d
|
K
)
=
{
f
|
K
:
f
∈
C
1
(
R
d
)
}
is always dense in $$C^1(K)$$
C
1
(
K
)
. The space $$C^1(K)$$
C
1
(
K
)
is then compared with other spaces of differentiable functions on compact sets.
Funder
Fonds De La Recherche Scientifique - FNRS
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Mathematics (miscellaneous)
Reference23 articles.
1. Whitney, H.: Analytic extensions of differentiable functions defined in closed sets. Trans. Am. Math. Soc. 36(1), 63–89 (1934)
2. Fefferman, C.L.: A sharp form of Whitney’s extension theorem. Ann. Math. (2) 161(1), 509–577 (2005)
3. Frerick, L., Jordá, E., Wengenroth, J.: Tame linear extension operators for smooth Whitney functions. J. Funct. Anal. 261(3), 591–603 (2011)
4. Frerick, L., Jordá, E., Wengenroth, J.: Whitney extension operators without loss of derivatives. Rev. Mat. Iberoam. 32(2), 377–390 (2016)
5. Frerick, L.: Extension operators for spaces of infinite differentiable Whitney jets. J. Reine Angew. Math. 602, 123–154 (2007)
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