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Acta Mathematica Sinica, English Series

, Volume 35, Issue 2, pp 245–256 | Cite as

Reconstruction of Splines from Nonuniform Samples

  • Qing Yue ZhangEmail author
  • Wen Chang Sun
Article
  • 25 Downloads

Abstract

In this paper, we study the reconstruction of spline functions from their nonuniform samples. We investigate the existence and uniqueness of the solution of the following problem: for given data {(xn, yn): n ∈ ℤ}, find a cardinal spline f(x), of a given degree, satisfying yn = f(xn), n ∈ ℤ. Several necessary and/or sufficient conditions for the existence and uniqueness of the solution of the problem are derived. Finally, an example and some applications are presented to illustrate the main results.

Keywords

Cardinal spline interpolation nonuniform sampling sampling set 

MR(2010) Subject Classification

94A20 94A12 42C15 

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science (CAS), Chinese Mathematical Society (CAS) and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of ScienceTianjin University of TechnologyTianjinP. R. China
  2. 2.School of Mathematical Sciences and LPMCNankai UniversityTianjinP. R. China

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