Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Contractions with Polynomial Characteristic Functions II. Analytic
  Approach   The simplest and most natural examples of completely nonunitary contractions
on separable complex Hilbert spaces which have polynomial characteristic
functions are the nilpotent operators. The main purpose of this paper is to
prove the following theorem: Let $T$ be a completely nonunitary contraction on
a Hilbert space $\mathcal{H}$. If the characteristic function $\Theta_T$ of $T$
is a polynomial of degree $m$, then there exist a Hilbert space $\mathcal{M}$,
a nilpotent operator $N$ of order $m$, a coisometry $V_1 \in
\mathcal{L}(\overline{ran} (I - N N^*) \oplus \mathcal{M}, \overline{ran} (I -
T T^*))$, and an isometry $V_2 \in \mathcal{L}(\overline{ran} (I - T^* T),
\overline{ran} (I - N^* N) \oplus \mathcal{M})$, such that \[ \Theta_T = V_1
\begin{bmatrix} \Theta_N & 0 0 & I_{\mathcal{M}} \end{bmatrix} V_2. \]

21
The categories of this paper are: adap-org
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The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics