摘要
This paper concerns the reconstruction of a function f in the Hardy space of the unit disc D by using a sample value f(a)and certain n-intensity measurements|<f,E_(a1…an)>|,where a_(1)…a_(n)∈D,and E_(a1…an)is the n-th term of the Gram-Schmidt orthogonalization of the Szego kernels k_(a1),k_(an),or their multiple forms.Three schemes are presented.The first two schemes each directly obtain all the function values f(z).In the first one we use Nevanlinna’s inner and outer function factorization which merely requires the 1-intensity measurements equivalent to know the modulus|f(z)|.In the second scheme we do not use deep complex analysis,but require some 2-and 3-intensity measurements.The third scheme,as an application of AFD,gives sparse representation of f(z)converging quickly in the energy sense,depending on consecutively selected maximal n-intensity measurements|<f,E_(a1…an)>|.
作者
曲伟
钱涛
邓冠铁
李尤发
周春旭
Wei QU;Tao QIAN;Guantie DENG;Youfa LI;Chunxu ZHOU(Department of Applied Mathematics,School of Mathematics and Physics,University of Science and Technology Beijing,Beijing,100083,China;Macao Center for Mathematical Sciences,Macao University of Science and Technolofy,Macao,China;School of Mathematical Sciences,Beijing Normal University,Beijing,100875,China;College of Mathematics and Information Science,Guangxi University,Nanning,530004,China)
基金
The Science and Technology Development Fund,Macao SAR(File no.0123/2018/A3)
supported by the Natural Science Foundation of China(61961003,61561006,11501132)
Natural Science Foundation of Guangxi(2016GXNSFAA380049)
the talent project of the Education Department of the Guangxi Government for one thousand Young-Middle-Aged backbone teachers
the Natural Science Foundation of China(12071035)。
