Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 1D Schr\"odinger operators with complex potentials   We consider a Schr\"odinger operator with complex-valued potentials on the
line. The operator has essential spectrum on the half-line plus eigenvalues
(counted with algebraic multiplicity) in the complex plane without the positive
half-line. We determine series of trace formulas. Here we have the new term: a
singular measure, which is absent for real potentials. Moreover, we estimate of
sum of Im part of eigenvalues plus singular measure in terms of the norm of
potentials. The proof is based on classical results about the Hardy spaces.

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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
3
The categories of this paper are: physics
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The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con