大连理工大学数学科学学院
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【中国科学院大学】Oscillatory Integral and Newton Polyhedron

2020年07月07日 14:44  点击:[]

报告题目: Oscillatory Integral and Newton Polyhedron

报告人:燕敦验教授(中国科学院大学

报告时间:2020710日(周五)9:00—10:00

腾讯会议 ID:971 925 751密码:200710

报告摘要:In this talk, we will introduce a class of oscillatory integral operators with the kernel being smooth function and compact support. Stein and Phong systematically investigated those operators and obtained the sharp $L^2$ decay estimates. Stein's results answered an important conjecture which was put by the distinguished mathematician Arnold. That is, the sharp decay estimate is determined by the Newton polyhedron of the phase function of the oscillatory integral. Finally, we give the sharp $L^p$ decay estimates of the oscillatory integral operators with homogeneous polynomial phases. As a consequence, we also give a sharp $L^p$-boundedness of the generalized Fourier transform.

报告人简介:燕敦验, 中国科学院大学本科部部长兼书记,教授、博士生导师,校学术委员会委员。主要研究方向:调和分析,应用与计算调和分析。主持三项国家自然科学基金面上项目;主持一项广东省与中国科学院的省院合作项目;参加一项国家自然科学基金重点项目、三项国家自然科学基金面上项目及一项中国科学院知识创新重点项目等重要研究课题。已在国内外学术期刊上发表研究论文60余篇,SCI50篇。

 

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