Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smooth extension of functions on a certain class of non-separable Banach
  spaces   Let us consider a Banach space $X$ with the property that every real-valued
Lipschitz function $f$ can be uniformly approximated by a Lipschitz,
$C^1$-smooth function $g$ with $\Lip(g)\le C \Lip(f)$ (with $C$ depending only
on the space $X$). This is the case for a Banach space $X$ bi-Lipschitz
homeomorphic to a subset of $c_0(\Gamma)$, for some set $\Gamma$, such that the
coordinate functions of the homeomorphism are $C^1$-smooth. Then, we prove that
for every closed subspace $Y\subset X$ and every $C^1$-smooth (Lipschitz)
function $f:Y\to\Real$, there is a $C^1$-smooth (Lipschitz, respectively)
extension of $f$ to $X$. We also study $C^1$-smooth extensions of real-valued
functions defined on closed subsets of $X$.

14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph