Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A condition for purely absolutely continuous spectrum for CMV operators
  using the density of states   We prove an averaging formula for the derivative of the absolutely continuous
part of the density of states measure for an ergodic family of CMV matrices. As
a consequence, we show that the spectral type of such a family is almost surely
purely absolutely continuous if and only if the density of states is absolutely
continuous and the Lyapunov exponent vanishes almost everywhere with respect to
the same. Both of these results are CMV operator analogues of theorems obtained
by Kotani for Schr\"odinger operators.

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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th