Adaptive Fourier series - a variation of greedy algorithm

@article{Qian2011AdaptiveFS,
  title={Adaptive Fourier series - a variation of greedy algorithm},
  author={Tao Qian and Yanbo Wang},
  journal={Adv. Comput. Math.},
  year={2011},
  volume={34},
  pages={279-293}
}
We study decomposition of functions in the Hardy space H2(D) into linear combinations of the basic functions (modified Blaschke products) in the system Bn(z) = √ 1− |an|2 1− anz n−1 ∏ k=1 z − ak 1− akz , n = 1, 2, ..., (1) where the points an’s in the unit disc D are adaptively chosen in relation to the function to be decomposed. The chosen points an’s do not necessarily satisfy the usually assumed hyperbolic non-separability condition ∞ ∑ k=1 (1− |ak|) = ∞ (2) in the traditional studies of the… CONTINUE READING
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