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Approximation properties of wavelets and relations among scaling moments. II. (English) Zbl 1081.42027

The author derives a new orthonormality condition for orthogonal low-pass filters. Based on this condition, he then presents some interesting formulae for discrete scaling moments and for continuous scaling moments.
[See also Part I by the same author in Numer. Funct. Anal. Optimization 25, No. 6, 503–513 (2004; Zbl 1069.42022).]

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
65T60 Numerical methods for wavelets

Citations:

Zbl 1069.42022
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References:

[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.; · Zbl 0848.42021
[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.; · Zbl 0976.65124
[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.; · Zbl 0776.42018
[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.; · Zbl 0897.42019
[6] G. Strang, T. Nguyen: “Wavelets and Filter Banks — Gilbert Strang”, Wellesley-Cambridge Press, Vol. XXI, (1996), pp. 474.; · Zbl 1254.94002
[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. http://dx.doi.org/10.1137/0731065; · Zbl 0822.65013
[8] P. Wojtaszczyk: “A Mathematical introduction to wavelets”, London Mathematical Society Student Text, Cambridge University Press, Vol. 37, (1997), pp. 261.; · Zbl 0865.42026
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