A new factorization technique of the matrix mask of univariate refinable functions

Numerische Mathematik

Volumn 87, Issue 3, 2001, Pages 555-595

  Plonka, Gerlind ^a   Amos, Ron ^b  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

^b University of Wisconsin Madison   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040374496     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00005424     Document Type: Article

References (20)

1. d). Trans. Amer. Math. Soc. 341, 787-806 (1994)
2. d). J. Funct. Anal. 119, 37-78 (1994)
3. d). Constr. Approx. 14, 631-652 (1998)
4. [CDP] Cohen, A., I. Daubechies, and G. Plonka, Regularity of refinable function vectors. J. Fourier Anal. Anal. 3, 295-324 (1997)
5. [DM] Dahmen, W., and C. A. Micchelli, Biorthogonal wavelet expansions. Constr. Approx. 13, 293-328 (1997)
6. [GHM] Geronimo, J. S., D. P. Hardin, and P. R. Massopust, Fractal functions and wavelet expansions based on several scaling functions. J. Approx. Theory 78, 373-401 (1994)
7. [HC] Heil, C., and D. Colella, Matrix refinement equations: Existence and uniqueness. J. Fourier Anal. Anal. 2, 363-377 (1996)
8. [H] Hogan, T., Stability and independence of shifts of finitely many refinable functions. J. Fourier Anal. Appl. 3, 757-774 (1997)
9. [JM] Jia, R. Q, and C. A. Micchelli, Using the refinement equation for the construction of pre-wavelets II: powers of two, Curves and Surfaces. P. J. Laurent, A. Le Méhauté, and L. L. Schumaker (eds.) New York: Academic Press 1991, pp 209-246
10. [J] Jiang, Q., On the regularity of matrix refinable functions. SIAM J. Math. Anal. 29, 1157-1176 (1998)
11. [JS] Jiang, Q., and Z. Shen, On existence and weak stability of matrix refinable functions. Constr. Approx. 15, 337-353 (1999)
12. [MS] Micchelli, C. A., and T. Sauer, Regularity of multiwavelets. Adv. Comp. Math. 7, 455-545 (1997)
13. [P] Plonka, G., Approximation order provided by refinable function vectors. Constr. Approx. 13, 221-244 (1997)
14. Ron, A., Factorization theorems for univariate splines on regular grids. Israel J. Mathematics 70, 48-68 (1990)
15. Ron, A., Smooth refinable functions provide good approximation orders. SIAM J. Math. Anal. 28, 731-748 (1997)
16. Ron, A., Characterizations of linear independence and stability of the shifts of a univariate refinable function in terms of its refinement mask. CMS Tech. Rep. 93-3, University of Wisconsin-Madison, Sept. 92
17. [RS] Ron, A., and Z. Shen, The sobolev regularity of refinable functions (preprint 1997)
18. [S] Shen, Z., Refinable function vectors. SIAM J. Math. Anal. 29, 235-250 (1998)
19. [SF] Strang, G., and G. Fix, A Fourier analysis of the finite element variational method, Constructive Aspects of Functional Analysis (G. Geymonat, ed) C.I.M.E. II Ciclo, 1973, 793-840.
20. [SS] Strang, G., and V. Strela, Short wavelets and matrix dilation equations. IEEE Trans Acoustic., Speech, and Signal Processing 43, 108-115 (1995)