报告一：

题目： Fueter's Theorem, its motivation, generalisations, applications, and restrictions

时间： 星期四5月30日下午3:00–4:00

地点：5206

报告人： 钱涛（澳门科技大学教授）

摘要:   The talk will review the history in relation to Fueter’s theorem  that induce quaternionic regular functions from holomorphic functions of one complex variable. Developments of theme will be divided into trilogy correspond to the origination of Fueter, Sce’s generalization to odd dimensions and Qian’s. It will also include results in relation to harmonic functions and later axial monogenic functions. Apart from motivations, generalisations, applications we also spell out restrictions, as well as open questions. 

报告二：

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

时间： 星期四5月30日下午4:20–5:20

地点：5206

报告人：钱涛（澳门科技大学教授）

摘要：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. 

报告人简介：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多篇论文，出版多部研究著作，同时担任SCI数学期刊MMAS,CAOT,CVEE编委。