Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Meromorphic extensions from small families of circles and holomorphic
  extensions from spheres   Let B be the open unit ball in C^2 and let a, b, c be three points in C^2
which do not lie in a complex line, such that the complex line through a and b
meets B and such that <a|b> is different from 1 if one of the points a, b is in
B and the other in the complement of B and such that at least one of the
numbers <a|c>, <b|c> is different from 1. We prove that if a continuous
function f on the sphere bB extends holomorphically into B along each complex
line which passes through one of the points a, b, c then f extends
holomorphically through B. This generalizes recent work of L.Baracco who proved
such a result in the case when the points a, b, c are contained in B. The proof
is different from the one of Baracco and uses the following one variable result
which we also prove in the paper and which in the real analytic case follows
from the work of M.Agranovsky: Let D be the open unit disc in C. Given a in D
let C(a) be the family of all circles in D obtained as the images of circles
centered at the origin under an automorphism of D that maps the origin to a.
Given distinct points a, b in D and a positive integer n, a continuous function
f on the closed unit disc extends meromorphically from every circle T in either
C(a) or C(b) through the disc bounded by T with the only pole at the center of
T of degree not exceeding n if and only if f is of the form f(z) =
g_0(z)+g_1(z)\bar z +...+ g_n(z)\bar z^n where the functions g_0, g_1, ..., g_n
are holomorphic on D.

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The categories of this paper are: supr-con
16
The categories of this paper are: stat
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
3
The categories of this paper are: physics