Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On $C^{0}$-fine approximation of convex functions by real analytic
  convex functions   We show that $C^0$-fine approximation of convex functions by smooth (or real
analytic) convex functions on $\R^d$ is possible in general if and only if
$d=1$. Nevertheless, for $d\geq 2$ we give a characterization of the class of
convex functions on $\R^d$ which can be approximated by real analytic (or just
smoother) convex functions in the $C^0$-fine topology. It turns out that the
possibility of performing this kind of approximation is not determined by the
degree of local convexity or smoothness of the given function, but by its
global geometrical behavior. We give some applications concerning prescription
of (sub-)differential boundary data to convex real analytic functions, and
smooth surgery of convex bodies.

19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas