Journal of Mathematical Sciences

, Volume 198, Issue 6, pp 724–734 | Cite as

Integral Representations and Sharp Estimates of B φ -Splines

  • Yu. K. Dem’yanovich
  • I. G. Burova

We derive an integral representation of second order coordinate B φ -splines. Based on this representation, we obtain sharp estimates for such splines and show that the estimates are attained in the polynomial case. Bibliography: 3 titles.


Integral Representation Column Vector Sharp Estimate Approximate Relation Integration Order 
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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, “Calibration relations for nonpolynomial splines” [in Russian], Probl. Mat. Anal. 43, 51–67 (2009); English transl.: J. Math. Sci., New York 164, No. 3, 364–382 (2010).CrossRefMathSciNetGoogle Scholar
  3. 3.
    Yu. K. Dem’yanovich, Theory of Spline Wavelets [in Russian], St. Peteresb. State Univ. Press, St. Petersb. (2013).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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