Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operator-valued rational functions   In this paper we show that every inner divisor of the operator-valued
coordinate function, $zI_E$, is a Blaschke-Potapov factor. We also introduce a
notion of operator-valued "rational" function and then show that $\Delta$ is
two-sided inner and rational if and only if it can be represented as a finite
Blaschke-Potapov product; this extends to operator-valued functions the
well-known result proved by V.P. Potapov for matrix-valued functions.

22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th