【摘 要】
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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 ||,where a1,…,an ∈ D,and Ea1…an is the n-th term of the Gram-Schmidt orthogonalization of the Sz
【机 构】
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Department of Applied Mathematics,School of Mathematics and Physics,University of Science and Techno
论文部分内容阅读
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 ||,where a1,…,an ∈ D,and Ea1…an is the n-th term of the Gram-Schmidt orthogonalization of the Szeg(o) kernels ka1,…,kan,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 | |.
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