Central European Journal of Mathematics

, Volume 2, Issue 4, pp 605–613 | Cite as

Approximation properties of wavelets and relations among scaling moments II

  • Václav Finěk


A new orthonormality condition for scaling functions is derived. This condition shows a close connection between orthonormality and relations among discrete scaling moments. This new condition in connection with certain approximation properties of scaling functions enables to prove new relations among discrete scaling moments and consequently the same relations for continuous scaling moments.


Orthonormality wavelets approximation properties scaling moments 

MSC (2000)

65T60 42C40 


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  1. [1]
    A. Cohen, R.D. Ryan: “Wavelets and Multiscale Signal Processing (Transl. from the French)”. Applied Mathematics and Mathematical Computation, Vol. 11, (1995), pp. 232.zbMATHMathSciNetGoogle Scholar
  2. [2]
    A. Cohen: “Wavelet methods in numerical analysis. Ciarlet”, P.G.(ed.) et al., Handbook of numerical analysis, Vol. 7 (Part 3); Techniques of scientific computing (Part 3), Elsevier, (2000), pp. 417–711.Google Scholar
  3. [3]
    I. Daubechies: “Ten Lectures on Wavelets”, CMBMS-NSF Regional Conference Series in Applied Mathematics, 61, Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics, (1992), pp. 357.zbMATHGoogle Scholar
  4. [4]
    V. Finěk: “Approximation properties of wavelets and relations among scaling moments”, Numerical Functional Analysis and Optimization, (2002), [to appear]Google Scholar
  5. [5]
    A.K. Louis, P. Maass, A. Rieder: Wavelets — Theory and Applications, Wiley, Chichester, 1997.Google Scholar
  6. [6]
    G. Strang, T. Nguyen: “Wavelets and Filter Banks — Gilbert Strang”, Wellesley-Cambridge Press, Vol. XXI, (1996), pp. 474.Google Scholar
  7. [7]
    W. Sweldens, R. Piessens: “Quadrature formulae and asymptotic error expansions for wavelet approximations of smooth functions”, SIAM J. Numer. Anal., Vol. 31, (1994), pp. 1240–1264.zbMATHMathSciNetCrossRefGoogle Scholar
  8. [8]
    P. Wojtaszczyk: “A Mathematical introduction to wavelets”, London Mathematical Society Student Text, Cambridge University Press, Vol. 37, (1997), pp. 261.zbMATHMathSciNetGoogle Scholar

Copyright information

© Central European Science Journals 2004

Authors and Affiliations

  • Václav Finěk
    • 1
  1. 1.Institut für Numerische Mathematik, Fakultät Mathematik und NaturwissenschaftenTechnische Universitt DresdenDresden

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