报告题目：Inverse resonance scattering on rotationally symmetric manifolds
报告人：Evgeny Korotyaev 教授
邀请人：徐小川
报告时间：2023年9月1日（周五）上午10:00-11:00
报告地点：藕舫楼702
报告摘要：We discuss inverse resonance scattering for the Laplacian on a rotationally symmetric manifold M = (0,∞) × Y whose rotation radius is constant outside some compact interval. The Laplacian on M is unitarily equivalent to a direct sum of one-dimensional Schrodinger operators with compactly supported potentials on the half-line. We prove
• Asymptotics of counting function of resonances at large radius.
• The rotation radius is uniquely determined by its eigenvalues and resonances.
• There exists an algorithm to recover the rotation radius from its eigenvalues and resonances.
The proof is based on some non-linear real analytic isomorphism between two Hilbert spaces.
报告人简介：Evgeny Korotyaev，东北师范大学，前沿交叉研究院教授，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、薛定谔算子等方向的研究工作，在Invent. Math., Commun. Math. Phys.,Trans. Am. Math. Soc., Inverse Probl., JFA, JDE等期刊发表学术论文150余篇。
数学与统计学院
2023年8月29日