Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse uniqueness results for one-dimensional weighted Dirac operators   Given a one-dimensional weighted Dirac operator we can define a spectral
measure by virtue of singular Weyl-Titchmarsh-Kodaira theory. Using the theory
of de Branges spaces we show that the spectral measure uniquely determines the
Dirac operator up to a gauge transformation. Our result applies in particular
to radial Dirac operators and extends the classical results for Dirac operators
with one regular endpoint. Moreover, our result also improves the currently
known results for canonical (Hamiltonian) systems. If one endpoint is limit
circle case, we also establish corresponding two-spectra results.

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The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc