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.
