Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse problems with a general transfer condition   We consider a Sturm-Liouville operator on a finite interval as well as a
scattering problem on the real line both with transfer conditions at the
origin. On a finite interval we show that the the Titchmarsh-Weyl $m$-function
can be uniquely determined from two spectra for the same equation but with
varied boundary conditions at one end of the interval. In addition, we prove
that the $m$-function can also be uniquely reconstructed from one spectrum and
the corresponding norming constants. For the scattering problem on the real
line we assume that the potential has compact essential support. For a given
symmetric finite intervals containing the essential-support of the potential
and a pair of separated boundary conditions imposed at the ends of the
interval, the spectrum and corresponding norming constants can be uniquely
recoverable from the scattering data on $\R$. Consequently the potential and
transfer matrix can be determined.

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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: eess
25
The categories of this paper are: patt-sol