Finěk, Václav Approximation properties of wavelets and relations among scaling moments. II. (English) Zbl 1081.42027 Cent. Eur. J. Math. 2, No. 4, 605-613 (2004). 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).] Reviewer: Qingtang Jiang (Morgantown) Cited in 3 Documents MSC: 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems 65T60 Numerical methods for wavelets Keywords:orthonormality; wavelets; approximation properties; scaling moments Citations:Zbl 1069.42022 PDFBibTeX XMLCite \textit{V. Finěk}, Cent. Eur. J. Math. 2, No. 4, 605--613 (2004; Zbl 1081.42027) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.