Journal of Mathematical Sciences

, Volume 144, Issue 6, pp 4568–4580 | Cite as

On wavelet decomposition of Hermite type splines

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


We consider wavelet decompositions of spaces of Hermite type splines of class C1(α, β) that are defined by a 4-component vector-valued function ϕ(t) ∈ C1 (α, β) by means of a grid X (not necessarily uniform) on (α, β) ∈ ℝ1 (the special case ϕ(t)def = (1, t, t2,t3)T corresponds to cubic Hermite splines). The basis wavelets obtained are compactly supported. The decomposition and reconstruction formulas are given. Bibliography: 8 titles.


Wavelet Decomposition Basis Wavelet Wavelet Theory Nonuniform Grid Spline Space 
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  1. 1.
    Yu. K. Dem’yanovich, Local Approximation on a Manifold and Minimal Splines [in Russian]Google Scholar
  2. 2.
    Yu. K. Dem’yanovich, Wavelets and Minimal Splines [in Russian], St.Petersburg Univ., 2003.Google Scholar
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    Yu. K. Dem’yanovich, “Smoothness of space of splines and wavelet decompositions” [in Russian], Dokl. Ros. Akad. Nauk, 401 (2005), no. 4, 1–4.Google Scholar
  5. 5.
    Yu. K. Dem’yanovich and A. A. Makarov, “Calibration relations for nonpolynomial splines” [in Russian], Prob. Mat. Anal 34 (2006), 39–54; English transl.: J. Math. Sci., New York 142 (2007), no. 1, 1769–1787.Google Scholar
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    Yu. K. Dem’yanovich, “Wavelet decompositions on a nonuniform grid” [in Russian], Trudy S.-Peterburg. Mat. O-va, 13 (2007), 27–51.Google Scholar
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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • Yu. K. Dem’yanovich
    • 1
  • A. V. Zimin
    • 1
  1. 1.St.Petersburg State UniversityRussia

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