Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schur parameters, Toeplitz matrices, and Kre\u{\i}n shorted operators   We establish connections between Schur parameters of the Schur class
operator-valued functions, the corresponding simple conservative realizations,
lower triangular Toeplitz matrices, and Kre\u\i n shorted operators. By means
of Schur parameters or shorted operators for defect operators of Toeplitz
matrices necessary and sufficient conditions for a simple conservative
discrete-time system to be controllable/observable and for a completely
non-unitary contraction to be completely non-isometric/completely
non-co-isometric are obtained. For the Schur problem a characterization of
central solution and uniqueness criteria to the solution are given in terms of
shorted operators for defect operators of contractive Toeplitz matrices,
corresponding to data.

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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc