Oscillatory Integral and Newton Polyhedron
报告题目(Title)：Oscillatory Integral and Newton Polyhedron
报告人(Speaker)：燕敦验 教授 （中国科学院大学）
地点(Place)：腾讯会议 692 165 517
时间(Time)：2020年6月19日 16:00-17:00
邀请人(Inviter)：薛庆营
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 systematacially investigated those operators and obtained the sharp $L^2$ decay estimates. In fact, Stein's results answered an important conjecture which was put by the distinguished mathematician Arnold. That is, the sharp decay estimate is determinated 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 sharp $L^p$-boundedness of the generalized Fourier transform.
主讲人简介
燕敦验, 中国科学院大学本科部部长，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。主持两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50余篇，SCI近40篇。
