HomeEventsColloquiumOthers 》 Content

Tao Qian: Adaptive Fourier Decomposition of one complex variable and generalizations to several complex variables and hyper complex cases

2024-05-30 09:27:06
报告人 时间 15:30-17:00
地点 E4-201 2024
月日 06-04

Time:15:30-17:00, Tuesday, June 4 2024

Venue:E4-201, Yungu Campus


Host: Zipeng Wang, ITS

Speaker:Tao Qian, Macau University of Science and Technology

Biography:钱涛,澳门科技大学教授,澳门数学研究中心主任,博士生导师。1984年博士毕业于北京大学。研究兴趣包括调和分析,信号分析,单与多复变量之复分析,四元数及Cilfford分析,随机过程等。近年来的主要研究课题为自适应Fourier分解及其应用。其中名为“瞬变信号的自适应正频率分解及算法实现”于2012获得澳门自然科学一等奖。迄今发表200余篇国际数学杂志论文,出版多部研究著作,同时担任SCI数学期刊MMAS, CAOT, CVEE编委。

Title:Adaptive Fourier Decomposition of one complex variable and generalizations to several complex variables and hyper complex cases

Abstract:The talk will present, including necessary details of, Adaptive Fourier Decomposition (AFD) of one complex variable eases. It then gives a number of successful generalizations and a number of failures as well. The key words include sparse representation by dictionary elements, Szegö kernels, reproducing kernel Hilbert space, boundary vanishing property, greedy algorithm and energy matching pursuit, pre-orthogonal AFD, rational approximation and Takenaka-Malmquist system, Blaschke products, scalar and matrix-valued Hardy spaces, Gram-Schmidt orthogonalization with Clifford algebra, etc.