Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new characterization of convexity with respect to Chebyshev systems   The notion of $n$th order convexity in the sense of Hopf and Popoviciu is
defined via the nonnegativity of the $(n+1)$st order divided differences of a
given real-valued function. In view of the well-known recursive formula for
divided differences, the nonnegativity of $(n+1)$st order divided differences
is equivalent to the $(n-k-1)$st order convexity of the $k$th order divided
differences which provides a characterization of $n$th order convexity.
  The aim of this paper is to apply the notion of higher-order divided
differences in the context of convexity with respect to Chebyshev systems
introduced by Karlin in 1968. Using a determinant identity of Sylvester, we
then establish a formula for the generalized divided differences which enables
us to obtain a new characterization of convexity with respect to Chebyshev
systems. Our result generalizes that of W\k{a}sowicz which was obtained in
2006. As an application, we derive a necessary condition for functions which
can be written as the difference of two functions convex with respect to a
given Chebyshev system.

14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin