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On translation invariant operators which preserve the B-spline recurrence

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Abstract

It was observed in [4] that the Hilbert transform of the univariate B-spline preserves the B-spline recurrence. Motivated by this observation, we characterize translation invariant operators that preserve the multivariate B-spline recurrence and analogous results are also provided for the multivariate cube spline.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, State University of New York, The University at Albany, Albany, NY, 12222, USA

    Charles A. Micchelli

  2. Department of Mathematics, Syracuse University, Syracuse, NY, 13244, USA

    Yuesheng Xu

  3. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Haizhang Zhang

Authors
  1. Charles A. Micchelli
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  2. Yuesheng Xu
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  3. Haizhang Zhang
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Corresponding author

Correspondence to Yuesheng Xu.

Additional information

Dedicated to Carl de Boor with appreciation for his insight into B-splines.

Charles A. Micchelli was supported in part by the US National Science of Foundation under grant CCR-0407476.

Yuesheng Xu was supported in part by the US National Science Foundation under grant CCR-0407476, by the Natural Science Foundation of China under grant 10371122, by the Chinese Academy of Sciences under the program “One Hundred Distinguished Chinese Scientists” and by Ministry of Education, People’s Republic of China, under the Changjian Scholarship through Zhongshan University.

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Micchelli, C.A., Xu, Y. & Zhang, H. On translation invariant operators which preserve the B-spline recurrence. Adv Comput Math 28, 157–169 (2008). https://doi.org/10.1007/s10444-006-9018-z

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  • DOI: https://doi.org/10.1007/s10444-006-9018-z

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