Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical Lieb-Thirring Bounds in Gaps and the Generalized Nevai
  Conjecture for Finite Gap Jacobi Matrices   We prove bounds of the form $\sum_{e\in I\cap\sigma_\di (H)} \dist
(e,\sigma_\e (H))^{1/2} \leq L^1$-norm of a perturbation, where $I$ is a gap.
Included are gaps in continuum one-dimensional periodic Schr\"odinger operators
and finite gap Jacobi matrices where we get a generalized Nevai conjecture
about an $L^1$ condition implying a Szeg\H{o} condition. One key is a general
new form of the Birman--Schwinger bound in gaps.

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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org