Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Caratheodory type representation with unit weights and related
  approximation problems   For arbitrary $n$ complex numbers $a_{\nu-1}$, $\nu=1,\dots,n$, where $n$ is
sufficiently large, we get the representation in the form of power sums:
$a_{\nu-1}=\lambda_1^\nu+\dots+\lambda_{2n+1}^\nu$, where $\lambda_k$ are
distinct points, such that $|\lambda_k|=1$. We study several applications to
the problem of approximation by exponential sums and by $h$-sums, to the
problem of extracting of harmonics from trigonometric polynomials. The result
is based on an estimate for the uniform approximation rate of bounded analytic
in the unit disk functions by logarithmic derivatives of polynomials, all of
whose zeros lie on the unit circle $C : |z| = 1$. Our result is a modification
of classical Carath\'eodory representation $a_{\nu-1}=\sum_{k=1}^{n} X_k
\lambda_k^\nu$, $\nu=1,2,\dots,n$, where weights $X_k\ge 0$, and $\lambda_k$
are distinct points, such that $|\lambda_k|=1$.

35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg