报告题目1: Analytic instantaneous frequency and mono-component function theory

报告摘要: Raised by signal analysts we present here a generalisation of the Fourier type  frequency concept based on trigonometric functions. We define analytic instantaneous frequency and form mono-component function theory. The topic is closely related to complex analysis as well as harmonic analysis, with the key words Moebius transform, Blaschke product, inner and outer functions, etc. We present some new results in relation to boundary phase derivative with applications in signal analysis. 

报告题目2: Adaptive Fourier Decomposition

报告摘要: Motivated by positive frequency decomposition the so called adaptive Fourier decomposition (AFD) was first proposed in around 2011. AFD is a type of sparse representation of signals in the complex Hardy H2 space by the parameterised Szego dictionary elements. It is a  matching pursuit methodology more sophisticated and effective than the general greedy algorithm.  AFD is subsequently extended into general Hilbert spaces with a dictionary enjoying boundary vanishing condition (BVC), called pre-orthogonal AFD (POAFD). It then was generalised to solve the $n$-Best approximation (n-Best) equivalent to the best approximation by rational functions of degree not exceeding $n$. 

报 告 人: 钱涛教授，澳门科技大学

报告时间: 2023年3月30日8:00-10:30

报告地点: 20幢306

报告人简介: 钱涛，澳门科技大学教授，博士生导师，澳门数学研究中心主任。1984年北京大学获博士学位，1984-2000年先后于中国科学院数学与系统科学研究所，麦考瑞大学，弗林德斯大学，新英格兰大学从事教学及研究工作，2000-2019年澳门大学数学系任教，2013年起为澳门大学特聘教授。研究方向为调和分析，复分析，Clifford分析，信号分析与图像处理。迄今为止在Automatica、Math. Ann.、J. Funct. Anal.、Tran. Amer. Math, Soc.、IEEE Transactions on Automatic Control、IEEE Transactions on Image Processing国际知名期刊上发表论文200多篇，出版专著2部，主持科研项目30余项， 担任Math. Meth. Appli. Sci.、Complex Anal. Oper. Theory、Complex Varia. Ellip. Equations等SCI杂志副主编。多次组织举办具有影响力的国际学术会议，与多国数学家有广泛合作与交流。

邀请人: 陈杰诚