Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Gleason solution model for row contractions   In the deBranges-Rovnyak functional model for contractions on Hilbert space,
any completely non-coisometric (CNC) contraction is represented as the adjoint
of the restriction of the backward shift to a deBranges-Rovnyak space,
$\mathscr{H} (b)$, associated to a contractive analytic operator-valued
function, $b$, on the open unit disk.
  We extend this model to a large class of CNC row contractions of several
copies of a Hilbert space into itself (including all CNC row contractions with
commuting component operators). Namely, we completely characterize the set of
all CNC row contractions, $T$, which are unitarily equivalent to an extremal
Gleason solution for a deBranges-Rovnyak space, $\mathscr{H} (b_T)$,
contractively contained in a vector-valued Drury-Arveson space of analytic
functions on the open unit ball in several complex dimensions. Here, a Gleason
solution is the appropriate several-variable analogue of the adjoint of the
restricted backward shift and the characteristic function, $b_T$, belongs to
the several-variable Schur class of contractive multipliers between
vector-valued Drury-Arveson spaces. The characteristic function, $b_T$, is a
unitary invariant, and we further characterize a natural sub-class of CNC row
contractions for which it is a complete unitary invariant.

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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: cs