Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized reflection coefficients   I consider general reflection coefficients for arbitrary one-dimensional
whole line differential or difference operators of order $2$. These reflection
coefficients are semicontinuous functions of the operator: their absolute value
can only go down when limits are taken. This implies a corresponding
semicontinuity result for the absolutely continuous spectrum, which applies to
a very large class of maps. In particular, we can consider shift maps (thus
recovering and generalizing a result of Last-Simon) and flows of the Toda and
KdV hierarchies (this is new). Finally, I evaluate an attempt at finding a
similar general setup that gives the much stronger conclusion of reflectionless
limit operators in more specialized situations.

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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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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: q-alg
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The categories of this paper are: mtrl-th