Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The theory of Hahn meromorphic functions, a holomorphic Fredholm theorem
  and its applications   We introduce a class of functions near zero on the logarithmic cover of the
complex plane that have convergent expansions into generalized power series.
The construction covers cases where non-integer powers of $z$ and also terms
containing $\log z$ can appear. We show that under natural assumptions some
important theorems from complex analysis carry over to the class of these
functions. In particular it is possible to define a field of functions that
generalize meromorphic functions and one can formulate an analytic Fredholm
theorem in this class. We show that this modified analytic Fredholm theorem can
be applied in spectral theory to prove convergent expansions of the resolvent
for Bessel type operators and Laplace-Beltrami operators for manifolds that are
Euclidean at infinity. These results are important in scattering theory as they
are the key step to establish analyticity of the scattering matrix and the
existence of generalized eigenfunctions at points in the spectrum.

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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: econ
20
The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga