TY  - JOUR
ID  - Mykytyuk2019
LB  - Mykytyuk2019
AU  - Mykytyuk, Yaroslav
AU  - Sushchyk, Nataliia
TI  - Description of the scattering data for Sturm-Liouville operators on the half-line
ST  - Description of the scattering data for Sturm-Liouville operators on the half-line
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2019
VL  - 39
IS  - 4
SP  - 557
EP  - 576
DO  - https://doi.org/10.7494/OpMath.2019.39.4.557
UR  - https://doi.org/10.7494/OpMath.2019.39.4.557
AB  - We describe the set of the scattering data for self-adjoint Sturm-Liouville operators on the half-line with potentials belonging to \(L_1(\mathbb{R}_+,\rho(x)\,\text{d} x)\), where \(\rho:\mathbb{R}_+\to\mathbb{R}_+\) is a monotonically nondecreasing function from some family \(\mathscr{R}\). In particular, \(\mathscr{R}\) includes the functions \(\rho(x)=(1+x)^{\alpha}\) with \(\alpha\geq 1\).
KW  - inverse scattering
KW  - Schrödinger operator
KW  - Banach algebra
SN  - 1232-9274
ER  -