Orthogonality Criteria for Multi-scaling Functions

Applied and Computational Harmonic Analysis

Volumn 5, Issue 3, 1998, Pages 277-311

  Lian, Jian Ao ^a  

^a PRAIRIE VIEW A AND M UNIVERSITY   (United States)

Author keywords

Compactly supported functions; Multi scaling functions; Multi wavelets; Orthonormality; Two scale matrix equations; Two scale matrix symbols

Indexed keywords

EID: 0141943748     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1006/acha.1997.0233     Document Type: Article

References (23)

1. C. K. Chui and J.-A. Lian, Construction of compactly supported symmetric and antisymmetric orthonormal wavelets with scale = 3, Appl. Comput. Harmon. Anal. 2 (1995), 21-51.
2. C. K. Chui and J.-A. Lian, A study of orthonormal multi-wavelets, J. Appl. Numer. Math. 20 (1996), 272-298.
3. A. Cohen, Ondelettes, analyses multirésolutions et filtres miroir en quadrature, Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990), 439-459.
4. A. Cohen, I. Daubechies, and J. C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math. 45 (1992), 485-560.
5. I. Daubechies, "Ten Lectures on Wavelets," CBMS-NSF Series in Applied Math 61, SIAM, Philadelphia, 1992.
6. I. Daubechies, Orthonormal basis of compactly supported wavelets, Comm. Pure Appl. Math. 41 (1988), 909-996.
7. J. S. Geronimo, D. P. Hardin, and P. R. Massopust, Fractal functions and wavelet expansions based on several scaling functions, J. Approx. Theory 78 (1994), 373-401.
8. K. Gröchenig, Orthogonality criteria for compactly supported scaling functions, Appl. Comput. Harmon. Anal. 1 (1994), 242-245.
9. T. N. T. Goodman and S. L. Lee, Wavelets of multiplicity r, Trans. Amer. Math. Soc. 342 (1994), 307-324.
10. C. Heil, G. Strang, and V. Strela, Approximation by translates of refinable functions, Numer. Math. 73 (1996) 75-94.
11. R. A. Horn and C. R. Johnson, "Topics in Matrix Analysis," Cambridge Univ. Press, Cambridge, UK, 1991.
12. R. Q. Jia and C. A. Micchelli, Using the refinement equations for the construction of pre-wavelets. II. Powers of two, in "Curves and Surfaces" (P. J. Laurent, A. Lé Méhauté, and L. L. Schumaker, Eds.), pp. 205-246, Academic Press, New York, 1991.
13. n, preprint.
14. W. Lawton, Tight frames of compactly supported wavelets, J. Math. Phys. 31 (1990), 1898-1901.
15. W. Lawton, Necessary and sufficient conditions for constructing orthonormal wavelet bases, J. Math. Phys. 32 (1991), 57-61.
16. W. Lawton, S. L. Lee, and Z. Shen, Stability and orthonormality of multidimensional refinable functions, SIAM J. Math. Anal., to appear.
17. J.-A. Lian, Characterization of the order of polynomial-reproduction for multi-scaling functions, in "Approximation Theory VIII" (C. K. Chui and L. L. Schumaker, Eds.), pp. 251-258, World Scientific, Singapore, 1995.
18. J.-A. Lian, On the order of polynomial reproduction for multi-scaling functions, Appl. Comput. Harmon. Anal. 3 (1996), 358-365.
19. J.-A. Lian, "Orthonormal Multi-wavelets with Small Supports," CAT Report 368, Dec. 1995.
20. S. Mallat, Multiresolution approximation and wavelets, Trans. Amer. Math. Soc. 315 (1989), 69-88.
21. P. R. Massopust, D. K. Ruch, and P. J. Van Fleet, On the support properties of scaling vectors, Appl. Comput. Harmon. Anal. 3 (1996), 229-238.
22. G. Plonka, Approximation order provided by refinable function vectors, Constr. Approx., to appear.
23. G. Strang and V. Strela, Orthonormal multi-wavelets with vanishing moments, J. Opt. Eng. 33 (1994), 2104-2107.