Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weighted Hardy spaces: shift invariant and coinvariant subspaces, linear
  systems and operator model theory   The Sz.-Nagy--Foias model theory for $C_{\cdot 0}$ contraction operators
combined with the Beurling-Lax theorem establishes a correspondence between any
two of four kinds of objects: shift-invariant subspaces, operator-valued inner
functions, conservative discrete-time input/state/output linear systems, and
$C_{\cdot 0}$ Hilbert-space contraction operators. We discuss an analogue of
all these ideas in the context of weighted Hardy spaces over the unit disk and
an associated class of hypercontraction operators.

5
The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin