Journal of Mathematical Sciences

, Volume 207, Issue 5, pp 736–752 | Cite as

Spline-Wavelet Decomposition on an Interval

  • Yu. K. Dem’yanovichEmail author
  • B. G. Vager

For spline-wavelet representations of the second-order on an interval, conditions under which decomposition operators are independent of the order of elementary operations are established. The notion of k-localized systems of functionals is introduced, and the operator set in which the embedding operator possesses a unique left inverse is studied. Bibliography: 3 titles.


Column Vector Coarsened Grid Linear Independence Elementary Operation Spline Space 
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  1. 1.
    Yu. K. Dem’yanovich and O. M. Kosogorov, “Calibration relations for nonpolynomial splines,” Probl. Matem. Anal., 43, 3–19 (2009).Google Scholar
  2. 2.
    Yu. K. Dem’yanovich, “Nonsmooth spline-wavelet expansions and their properties,” Zap. Nauchn. Semin. POMI, 395, 31–60 (2012).MathSciNetGoogle Scholar
  3. 3.
    Yu. K. Dem’yanovich, The Theory of Spline - Wavelets [in Russian], SPbGU, St. Petersburg (2013).Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.St.Petersburg State UniversitySt.PetersburgRussia
  2. 2.St.Petersburg State Architecture-Building UniversitySt.PetersburgRussia

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