# Approximation properties of wavelets and relations among scaling moments II

Open Mathematics (2004)

- Volume: 2, Issue: 4, page 605-613
- ISSN: 2391-5455

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topVáclav Finěk. "Approximation properties of wavelets and relations among scaling moments II." Open Mathematics 2.4 (2004): 605-613. <http://eudml.org/doc/268835>.

@article{VáclavFiněk2004,

abstract = {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.},

author = {Václav Finěk},

journal = {Open Mathematics},

keywords = {65T60; 42C40},

language = {eng},

number = {4},

pages = {605-613},

title = {Approximation properties of wavelets and relations among scaling moments II},

url = {http://eudml.org/doc/268835},

volume = {2},

year = {2004},

}

TY - JOUR

AU - Václav Finěk

TI - Approximation properties of wavelets and relations among scaling moments II

JO - Open Mathematics

PY - 2004

VL - 2

IS - 4

SP - 605

EP - 613

AB - 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.

LA - eng

KW - 65T60; 42C40

UR - http://eudml.org/doc/268835

ER -

## References

top- [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. Zbl0848.42021
- [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.
- [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. Zbl0776.42018
- [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. Zbl0897.42019
- [6] G. Strang, T. Nguyen: “Wavelets and Filter Banks - Gilbert Strang”, Wellesley-Cambridge Press, Vol. XXI, (1996), pp. 474. Zbl1254.94002
- [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 Zbl0822.65013
- [8] P. Wojtaszczyk: “A Mathematical introduction to wavelets”, London Mathematical Society Student Text, Cambridge University Press, Vol. 37, (1997), pp. 261. Zbl0865.42026

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