All Questions
Tagged with lipschitz-spaces smoothness
2 questions
4
votes
1
answer
500
views
Smooth approximation of the $\max\{0,x\}$ function with controlled derivatives
Motivation/Hand-Wavy Question:
In this post, it was asked what the best local approximation of $f(x):=\max\{0,x\}$ is by a polynomial of a given degree; with the answer provided by Chebyshev's ...
3
votes
0
answers
171
views
Covering number $C^k$-balls in $C(\mathbb{R}^n)$
Fix a positive integer $n$ and and an non-negative integer $k$. The Arzela-Ascoli theorem guarantees that for a given positive integer $k$ and a given $L>0$ the set
$$
Ball_{C^{k,1}([0,1]^n)}(0,L)
...