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甬江数学讲坛179讲(2021年第38讲)
2021-09-09 09:06     (点击:)

报告题目:The scattering of fractional Schrödinger operators with short range potentials

人: 黄天骁(中山大学 副教授)

会议时间:2021/9/13  上午11:30开始

会议地点:腾讯会议线上报告

会议链接:https://meeting.tencent.com/dm/6grYEHHMPJei?rs=25

会议 ID106 472 397

报告摘要: I will first review some basic concepts and classical results in the short range scattering theory for the Schrödinger operator , along with a brief introduction of the short range perturbation theory for simply characteristic operators including the higher order Schrödinger operators typically. Then I will explain how to establish the short range scattering theory for the fractional Schrödinger operator in the full range . When is not even, the challenge comes from the non-local aspect of , and the crucial study of its limiting absorption principle is related to a sharp Fourier restriction property. I will also give explicit examples on the non-existence of wave operators, to show that our short range condition is sharp with respect to the decay assumption on , where the decay threshold is new. This is a joint-work with Rui Zhang and Quan Zheng.

个人简介: 黄天骁本科与博士毕业于华中科技大学数学与统计学院,现为中山大学数学学院(珠海)副研究员,研究方向为调和分析及其在高阶和分数阶色散方程中的应用,主要工作发表于JFA, JDE, CPDE等国际一流期刊。其在高阶薛定谔算子相关的函数空间估计,一致预解式估计,唯一延拓性,散射理论等取得了系列成果,得到国际同行的广泛引用与好评。

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