Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A pre-order and an equivalence relation on Schur class functions and
  their invariance under linear fractional transformations   Motivated by work of Yu.L. Shmul'yan a pre-order and an equivalence relation
on the set of operator-valued Schur class functions are introduced and the
behavior of Redheffer linear fractional transformations (LFTs) with respect to
these relations is studied. In particular, it is shown that Redheffer LFTs
preserve the equivalence relation, but not necessarily the pre-order. The
latter does occur under some additional assumptions on the coefficients in the
Redheffer LFT.

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The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio