Oscillatory Integral and Newton Polyhedron
杰出校友论坛之二
报告题目(Title)：Oscillatory Integral and Newton Polyhedron
报告人(Speaker)：燕敦验 （中国科学院大学）
地点(Place)：后主楼12层1223
时间(Time)：2019年12月27日 13:00-14:00
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 obtain the sharp $L^p$ decay estimates of the oscillatory integral operators with homogeneous polynomial phases and real analytic function phases. Furthermore, we also consider the sharp $L^p$ decay estimates of the oscillatory integral on the high dimensional spaces. As a consequence, we also give sharp $L^p$-boundedness of the generalized Fourier transform.
主讲人简介
燕敦验, 男，理学博士，北京师范大学88届校友，现任中国科学院大学教授，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。主持多项项国家级项目，如自然科学基金面上项目等。已在国内外学术期刊上发表研究论文50余篇，与他人合作在国外出版学术专著两部，翻译美国科学院院士、Wolf奖得主Elias M.Stein等人的专著《Fourier Analysis: An Introduction》一部。2014年，荣获宝钢优秀教师奖。
