×

A study of orthonormal multi-wavelets. (English) Zbl 0877.65098

The authors introduce a general scheme for constructing symmetric and/or antisymmetric compactly supported orthonormal multiscaling functions and multi-wavelets, and give some applications.
Reviewer: K.Trimeche (Tunis)

MSC:

65T60 Numerical methods for wavelets
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Chui, C. K., An Introduction to Wavelets (1992), Academic Press: Academic Press Boston · Zbl 0925.42016
[2] Chui, C. K.; Wang, J. R., Orthonormal wavelets with the same support and multiplicity τ to increase the number of vanishing moments τ-fold, (Abstract Book, Texas Approx. Theory Conference, VIII (1995))
[3] Chui, C. K.; Wang, J. Z., On compactly supported spline wavelets and duality principle, Trans. Amer. Math. Soc., 330, 903-916 (1992) · Zbl 0759.41008
[4] Daubechies, I., Orthonormal basis of compactly supported wavelets, Comm. Pure Appl. Math., 41, 909-996 (1988) · Zbl 0644.42026
[5] Daubechies, I., Ten Lectures on Wavelets, (CBMS-NSF Series in Applied Math., 61 (1992), SIAm: SIAm Philadelphia, PA) · Zbl 0776.42018
[6] Geronimo, J. S.; Hardin, D. P.; Massopust, P. R., Fractal functions and wavelet expansions based on several scaling functions, J. Approx. Theory, 78, 373-401 (1994) · Zbl 0806.41016
[7] Goodman, T. N.T., Interpolatory Hermite spline wavelets, J. Approx. Theory, 78, 174-189 (1994) · Zbl 0805.41008
[8] Goodman, T. N.T.; Lee, S. L., Wavelets of multiplicity τ, Trans. Amer. Math. Soc., 342, 307-324 (1994) · Zbl 0799.41013
[9] Goodman, T. N.T.; Lee, S. L.; Tang, W. S., Wavelets in wandering subspaces, Trans. Amer. Math. Soc., 338, 639-654 (1993) · Zbl 0777.41011
[10] W. Lawton, S.L. Lee and Z. Shen, An algorithm for matrix extension and wavelet construction, Preprint.; W. Lawton, S.L. Lee and Z. Shen, An algorithm for matrix extension and wavelet construction, Preprint. · Zbl 0842.41011
[11] Lian, J. A., Characterization of the order of polynomial-reproduction for multi-scaling functions, (Chui, C. K.; Schumaker, L. L., Approx. Theory, VIII (1995), World Sci. Publ: World Sci. Publ Singapore), 251-258 · Zbl 0927.42024
[12] Massopust, P. R.; Ruch, D. K.; Van Fleet, P. J., On the support properties of scaling vectors, (CAT Report No. 335 (1994), Texas A&M University) · Zbl 0858.42023
[13] G. Strang and V. Strela, Short wavelets and matrix dilation equations, Preprint.; G. Strang and V. Strela, Short wavelets and matrix dilation equations, Preprint.
[14] G. Strang and V. Strela, Finite element multi-wavelets, Preprint.; G. Strang and V. Strela, Finite element multi-wavelets, Preprint. · Zbl 0857.65118
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.