Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sturm-Liouville-type operators with frozen argument and Chebyshev
  polynomials   The paper deals with Sturm-Liouville-type operators with frozen argument of
the form $\ell y:=-y''(x)+q(x)y(a),$ $y^{(\alpha)}(0)=y^{(\beta)}(1)=0,$ where
$\alpha,\beta\in\{0,1\}$ and $a\in[0,1]$ is an arbitrary fixed rational number.
Such nonlocal operators belong to the so-called loaded differential operators,
which often appear in mathematical physics. We focus on the inverse problem of
recovering the potential $q(x)$ from the spectrum of the operator $\ell.$ Our
goal is two-fold. Firstly, we establish a deep connection between the so-called
main equation of this inverse problem and Chebyshev polynomials of the first
and the second kinds. This connection gives a new perspective method for
solving the inverse problem. In particular, it allows one to completely
describe all non-degenerate and degenerate cases, i.e. when the solution of the
inverse problem is unique or not, respectively. Secondly, we give a complete
and convenient description of iso-spectral potentials in the space of
complex-valued integrable functions.

37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an