Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral and resonance problem for perturbations of periodic Jacobi
  operators   Necessary and sufficient conditions are presented for a measure to be the
spectral measure of a finite range or exponentially decaying perturbation of a
periodic Jacobi operator.
  As a corollary we can fully solve the inverse resonance problem: given
resonances and eigenvalues we can recover the spectral measure of the Jacobi
operator; we provide necessary and sufficient conditions under which such an
operator exists and is unique; and we show that the inverse resonance problem
is stable under small perturbations.

16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th