报告题目：Kernel Expansions in Reproducing Kernel Hilbert Spaces and Applications
A large class of Hilbert spaces belong to the category of reproducing kernel Hilbert space (RKHS), including Hardy spaces, band-limited Paley-Wiener classes, Sobolev spaces, weighted Bergman and weighted Hardy spaces, etc. In fact, ranges of general integral and differential operators arecall RKHS. This talk will introduce an approximation theory and algorithm, called pre-orthogonal adaptive Fourier decomposition, abbreviated as POAFD, in those RKHSs that possess what we call boundary vanishing property (BVP). The introduced POAFD is a generalization of AFD for Hardy spaces that stands as the fastest greedy algorithm. It has effective applications to signal and image analysis, as well as to system identification. It can well replace Fourier series and integral transforms, wavelet method, neural network, and compressive sensing in the involved applications.
报告人：Tao Qian Professor
Tao Qian, PhD 1984 Peking University, worked in Inst. of Systems Science of the Chinese Academy of Sciences from 1984 to 1986. Worked in Australia from 1986 to 2000 as postdoc fellow with A. McIntosh and G. Gaudry, and as Lecturer in New England University of NSW. From 2000 to now have been working in University of Macau, as Associate Professor, Professor, Head of Department of Mathematics, Distinguished Professor. Due to his studies on analytic instantaneous frequencies he obtained the first grade of natural science award in Macau in 2012. So far has published more than 200 research papers, monographs, edited books and conference proceedings, in international science presses.