Acta mathematica scientia,Series B ›› 2014, Vol. 34 ›› Issue (3): 660-672.doi: 10.1016/S0252-9602(14)60038-2

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MATCHING PURSUITS AMONG SHIFTED CAUCHY KERNELS IN HIGHER-DIMENSIONAL SPACES

QIAN Tao, WANG Jin-Xun*, YANG Yan   

  1. Department of Mathematics, University of Macau, Macao, China|School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, China
  • Received:2012-07-11 Revised:2013-10-09 Online:2014-05-20 Published:2014-05-20
  • Contact: WANG Jin-Xun|wjxpyh@gmail.com E-mail:fsttq@umac.mo; wjxpyh@gmail.com; mathyy@sina.com
  • About author:WANG Jin-Xun|wjxpyh@gmail.com
  • Supported by:

    This work was supported by Macao FDCT (098/2012/A3), Research Grant of the University of Macau (UL017/08-Y4/MAT/QT01/FST), National Natural Science Funds for Young Scholars (10901166), and Sun Yat-sen University Operating Costs of Basic Research Projects to Cultivate Young Teachers (11lgpy99).

Abstract:

Appealing to the Clifford analysis and matching pursuits, we study the adaptive decompositions of functions of several variables of finite energy under the dictionaries con-sisting of shifted Cauchy kernels. This is a realization of matching pursuits among shifted Cauchy kernels in higher-dimensional spaces. It offers a method to process signals in arbitrary
dimensions.

Key words: Hardy space, monogenic, adaptive decomposition, dictionary, matching pur-suit, optimal approximation by rational functions

CLC Number: 

  • 30G35
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