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4 votes
1 answer
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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 ...
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3 votes
0 answers
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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) ...
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