Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-self-adjoint operators, infinite determinants, and some applications   We study various spectral theoretic aspects of non-self-adjoint operators.
Specifically, we consider a class of factorable non-self-adjoint perturbations
of a given unperturbed non-self-adjoint operator and provide an in-depth study
of a variant of the Birman-Schwinger principle as well as local and global
Weinstein-Aronszajn formulas.
  Our applications include a study of suitably symmetrized (modified)
perturbation determinants of Schr\"odinger operators in dimensions n=1,2,3 and
their connection with Krein's spectral shift function in two- and
three-dimensional scattering theory. Moreover, we study an appropriate
multi-dimensional analog of the celebrated formula by Jost and Pais that
identifies Jost functions with suitable Fredholm (perturbation) determinants
and hence reduces the latter to simple Wronski determinants.

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The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol