Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Commuting row contractions with polynomial characteristic functions   A characteristic function is a special operator-valued analytic function
defined on the open unit ball of $\mathbb{C}^n$ associated with an $n$-tuple of
commuting row contraction on some Hilbert space. In this paper, we continue our
study of the representations of $n$-tuples of commuting row contractions on
Hilbert spaces, which have polynomial characteristic functions. Gleason's
problem plays an important role in the representations of row contractions. We
further complement the representations of our row contractions by proving
theorems concerning factorizations of characteristic functions. We also
emphasize the importance and the role of the noncommutative operator theory and
noncommutative varieties to the classification problem of polynomial
characteristic functions.

32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat