Approximation properties of wavelets and relations among scaling moments II

Václav Finěk 1
  • 1 Technische Universitt Dresden


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.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [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.

  • [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.

  • [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.

  • [4] V. Finěk: “Approximation properties of wavelets and relations among scaling moments”, Numerical Functional Analysis and Optimization, (2002), [to appear]

  • [5] A.K. Louis, P. Maass, A. Rieder: Wavelets — Theory and Applications, Wiley, Chichester, 1997.

  • [6] G. Strang, T. Nguyen: “Wavelets and Filter Banks — Gilbert Strang”, Wellesley-Cambridge Press, Vol. XXI, (1996), pp. 474.

  • [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.

  • [8] P. Wojtaszczyk: “A Mathematical introduction to wavelets”, London Mathematical Society Student Text, Cambridge University Press, Vol. 37, (1997), pp. 261.


Journal + Issues