报告人：夏永辉教授

报告题目：A dynamical system framework yielding quantitative inverse spectral results for Sturm–Liouville operators

报告摘要：This paper establishes a dynamical-system framework that yields quantitative results for the inverse optimal spectral problem of reconstructing a potential $\hat{q}$ from finite observed eigenvalues to achieve an optimal approximation of the target potential $q_0$. Previous efforts relying on convex analysis have been confined solely to {\em qualitative} analysis due to the inherent limitations of convex-analytic techniques for inverse problems, while the {\bf quantitative} counterpart has remained an open problem. Based on our dynamical-system framework, we provide a quantitative characterization of the relationship between the reconstructed potential $\hat{q}$, its target potential  $q_0$, and the observed eigenvalue $\lambda_*$. In particular, for ${q} \in \mathcal{L}^2$, our framework yields a substantially stronger conclusion. Remarkably, our dynamical-system framework secures the uniqueness of $\hat{q}$ over the full parameter space $(\lambda_*, q_0)$, liberating the theory from the prevailing constraint $\lambda_* > \lambda_1(q_0)$ (where $\lambda_*$ is the observed eigenvalue and $\lambda_1$ is the principle eigenvalue). This stands in sharp contrast to classical approaches, which rely heavily on convex-set analysis and are inherently confined by its stringent assumptions.

报告人简介：夏永辉，男、现为佛山大学教授，学科方向带头人。曾获省部级科技进步奖3项，其中浙江省科学技术进步一等奖1项, 获福建青年科技奖。入选闽江学者特聘教授；2012年入选浙江省“151人才工程”第二层次。2021年，2023年科技部重点研发计划答辩会评专家组成员。2024年国家青年人才会评专家。多次担任科技部、教育部以及各省市人才项目和科技奖励、基金项目的会评专家或通讯评议。主持国家自然科学基金4项(其中面上3项，青年1项)，参与国家重点1项，主持浙江省基金重点项目1项。曾任浙江师范大学“杰出学者”特聘教授、博士生导师，与合作者一起推广了著名学者庞加莱和李雅普诺夫关于二维平面系统可积的充要条件的经典理论,将此可积理论推广到了任意有限维；建立了四元数体上微分方程理论与应用的基本框架(已经形成专著在中国科学出版社出版)；改进了经典的全局Hartman-Grobman线性化定理； 在有限个节点信息的基础上，建立了一类全新Sturm-Liouville算子反节点问题的基本框架。在学科方向的权威杂志Math. Ann., JDE、JDDE、SIAM J Appl Math、Proc. Roy. Edinburg Sect. A, Studies Appl Math、中国科学等杂志上发表系列论文。H-index指数28，被引用2000余次。

报告时间：2026年8月21日15：00

报告形式：#腾讯会议：239-708-867