主讲人：Marius Tucsnak 教授
主持人：李韬 教授
开始时间：2018-6-4 14:00-15:00
讲座地址：闵行数学楼401报告厅
主办单位：数学科学学院 科技处

报告人简介：
M.Tucsnak 教授1985年在罗马尼亚布加勒斯特大学获得硕士学位，1992在法国奥尔良大学获博士学位。曾先后在罗马尼亚科学院，法国巴黎第十三大学和洛林大学工作。目前在法国波尔多大学工作并成为法国IUF资深成员。他的研究领域是控制理论（由偏微分方程主导）、分析学及流固耦合理论。他与G.Weiss 合作出版了专著《Observation and Control for Operator Semigroups》，并发表了80篇左右的学术论文。
报告内容简介：
  This work considers systems described by the heat equation on an interval  with L2 boundary controls at the two extremities. We study the reachable space at some fixed strictly positive time. Our main results assert that this space is generally sandwiched between two Hilbert spaces of holomorphic functions defined on a square in the complex plane and which has the initial segment as one of the diagonals. More precisely, we prove that the reachable space contains the Hardy-Smirnov space and it is contained in the Bergman space associated to the above mentioned square. The methodology, quite different of the one employed in previous literature, is a direct one. We first represent the input-to-state map as an integral operator whose kernel is a sum of Gaussians and then we study the range of this operator by combining the theory of Riesz bases for Smirnov spaces in polygons and the theory developed by Aikawa, Hayashi and Saitoh on the range of integral transforms, in particular those associated with the heat kernel.