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Characterizations of multi-knot piecewise linear spectral sequences

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We study two classes of orthonormal bases for \( L^{2} {\left[ {0,1} \right]} \) in this paper. The exponential parts of these bases are multi-knot piecewise linear functions. These bases are called spectral sequences. Characterizations of these multi-knot piecewise linear functions are provided. We also consider an opposite problem for single-knot piecewise linear spectral sequences, where the piecewise linear functions are defined on \( \left[ {0,\theta } \right) \) and \( {\left[ {\theta ,1} \right]} \). We show that such spectral sequences do not exist except for \( \theta = \frac{1} {2} \).

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Authors and Affiliations

  1. Research and Development Center, 501, China Academy of Railway Sciences, Daliu Shu No. 2, Haidian District, Beijing, 100081, PR China

    Haitao Li

  2. Academy of Mathematics and Systems Science, Chinese Academy of Science, East Road of Zhongguan Chun No. 55, Haidian District, Beijing, 100080, PR China

    Haitao Li

  3. School of Information Science and Engineering, Graduate School of the Chinese Academy of Sciences, Beijing, 100080, PR China

    Dunyan Yan

Authors
  1. Haitao Li
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  2. Dunyan Yan
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Correspondence to Dunyan Yan.

Additional information

*Supported by the Technology and Research project 2002YF015 of the Ministry of Railway of China and by the Natural Science Foundation of China under grant 10371122.

**Supported by the Presidential Foundation of Graduate School of the Chinese Academy of Sciences (yzjj200505).

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Li, H., Yan, D. Characterizations of multi-knot piecewise linear spectral sequences. Adv Comput Math 27, 401–422 (2007). https://doi.org/10.1007/s10444-005-9006-8

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