前沿论坛

报告题目：Inverse scattering for Schrödinger operators with compactly supported potentials on half line

报告人：Prof. Evgeny Korotyaev（圣彼得堡国立大学）

报告时间：2022年5月5日 北京时间 15:00-16:30

报告地点：Zoom会议 会议号：946 8369 0301  密码：123456

报告内容简介：

For Schrödinger operators with compactly supported potentials on the half line we prove the following results:

(1) The mapping from real compactly supported potentials to the associated Jost functions  (in some class of entire functions) is one-to-one and onto.

(2) We show that such a potential is uniquely determined by its eigenvalues and resonances. Moreover, the corresponding algorithm is presented.

(3) We take the value of the S-matrix on some infinite sequence of positive real numbers.Using this sequence obtained from S-matrix we recover uniquely the potential by a new explicit formula,without the Gelfand-Levi-tan-Marchenko equation.

报告人简介：Evgeny Korotyaev, 圣彼得堡国立大学，数学-力学系教授，俄罗斯高等经济研究大学兼职教授。1982年于圣彼得堡国立大学获PhD学位，1996年于圣彼得堡Steklov研究所获理学博士学位。长期致力于逆谱理论与可积系统、几何函数论、散射理论、（周期介质上的）薛定谔方程等方向的研究工作，发表学术论文150余篇。