Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bergman polynomials on an Archipelago: Estimates, Zeros and Shape
  Reconstruction   Growth estimates of complex orthogonal polynomials with respect to the area
measure supported by a disjoint union of planar Jordan domains (called, in
short, an archipelago) are obtained by a combination of methods of potential
theory and rational approximation theory. The study of the asymptotic behavior
of the roots of these polynomials reveals a surprisingly rich geometry, which
reflects three characteristics: the relative position of an island in the
archipelago, the analytic continuation picture of the Schwarz function of every
individual boundary and the singular points of the exterior Green function. By
way of explicit example, fine asymptotics are obtained for the lemniscate
archipelago $|z^m-1|<r^m, 0<r<1,$ which consists of $m$ islands. The asymptotic
analysis of the Christoffel functions associated to the same orthogonal
polynomials leads to a very accurate reconstruction algorithm of the shape of
the archipelago, knowing only finitely many of its power moments. This work
naturally complements a 1969 study by H. Widom of Szeg\H{o} orthogonal
polynomials on an archipelago and the more recent asymptotic analysis of
Bergman orthogonal polynomials unveiled by the last two authors and their
collaborators.

1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th