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Interpolation

  • Hua Loo Keng
  • Wang Yuan
Chapter

Abstract

Let 1 < n1<n2 ... be a sequence of integers and let
$$ {P_{{n_l}}}(k) = \left( {{x_1}^{\left( {{n^l}} \right)}(k),...,x_s^{\left( {{n_l}} \right)}(k)} \right),\quad 1 \leqslant k \leqslant {n_l},l = 1,2,... $$
be a sequence of uniformly distributed sets in G s . For any given function f(x) on G s , let
$$ {P_f}(x) = \sum\limits_{k = 1}^{{n_l}} f \left( {{P_{{n_l}}}(k)} \right){\varphi_{{n_l},k}}(x) $$
(9.1)
, where \( {\phi_{{{n_l},k}}}(x)\left( {1 \leqslant k \leqslant {n_1}} \right) \) are given functions.

Keywords

Error Term Number Theory Induction Hypothesis Fourier Coefficient Fourier Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg and Science Press. Beijing 1981

Authors and Affiliations

  • Hua Loo Keng
    • 1
  • Wang Yuan
    • 1
  1. 1.Institute of MathematicsAcademia SinicaBeijingThe People’s Republic of China

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