Description of the scattering data for Sturm-Liouville operators on the half-line

Opuscula Mathematica

article

Yaroslav Mykytyuk¹  Nataliia Sushchyk¹ 

[1] Lviv National University, 1 Universytets'ka Str.

关键词: inverse scattering;    Schrödinger operator;    Banach algebra.;   

DOI  :  10.7494/OpMath.2019.39.4.557

学科分类：环境科学（综合）

来源: AGH University of Science and Technology Press

【 摘 要 】

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 \(\alpha\geq 1\).

【 授权许可】

CC BY-NC