Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Absolute continuity for commuting row contractions   Absolutely continuous commuting row contractions admit a weak-$*$ continuous
functional calculus. Building on recent work describing the first and second
dual spaces of the closure of the polynomial multipliers on the Drury-Arveson
space, we give a complete characterization of these commuting row contractions
in measure theoretic terms. We also establish that completely non-unitary row
contractions are necessarily absolutely continuous, in direct parallel with the
case of a single contraction. Finally, we consider refinements of this question
for row contractions that are annihilated by a given ideal.

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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga