Journal of Mathematical Sciences

, Volume 202, Issue 2, pp 184–199 | Cite as

Biorthogonal Approximation by Splines

  • Yu. K. Dem’yanovich
  • A. V. Lebedeva

We establish two-sided boundary biorthogonal approximations of twice continuously differentiable functions by Bφ-splines of the second order. We obtain an integral representation for the remainder of biorthogonal approximations by quadratic splines. Based on these results, we derive error estimates for some problems of approximation and interpolation of Lagrange type. These estimates are attained in the polynomial case. Bibliography: 5 titles.


Integral Representation Interpolation Problem Approximate Relation Spline Space Quadratic Spline 
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  1. 1.
    S. Mallat, A Wavelet Tour of Signal Processing, Academic Press (1999).Google Scholar
  2. 2.
    Yu. K. Dem’yanovich and O. M. Kosogorov, “Spline-wavelet decompositions on open and closed intervals” [in Russian], Probl. Mat. Anal. 43, 69–87 (2009); English transl.: J. Math. Sci., New York 164, No. 3, 383–402 (2010).Google Scholar
  3. 3.
    Yu. K. Dem’yanovich, Theory of Spline Wavelets [in Russian], St. Peteresb. State Univ. Press, St. Petersb. (2013).Google Scholar
  4. 4.
    Yu. K. Dem’yanovich and I. G. Burova, “Integral representations and sharp estimates of -splines” [in Russian], Probl. Mat. Anal. 75, 61–69 (2014); English transl.: J. Math. Sci., New York 198, No. 6, 724–734 (2014).Google Scholar
  5. 5.
    Yu. K. Dem’yanovich, “Embedded spaces of trigonometric splines and their wavelet expansion” [in Russian], Mat. Zametki 78, No. 5, 658-675 (2005): English transl.: Math. Notes 78, No. 5, 615-630 (2005).Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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