Lp Solutions of Refinement Equations

Journal of Fourier Analysis and Applications

Volumn 7, Issue 2, 2001, Pages 143-167

  Jia, Rong Qing ^a   Lau, Ka Sing ^b   Zhou, Ding Xuan ^b  

^a UNIVERSITY OF ALBERTA   (Canada)

^b NONE

Author keywords

Joint spectral radii; Refinable functions; Refinement equations; Wavelets

Indexed keywords

EID: 0035738051     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02510421     Document Type: Article

References (31)

1. Cavaretta, A.S., Dahmen, W., and Micchelli, C.A. (1991). Stationary Subdivision, Memoirs of Am. Math. Soc., 93.
2. Cohen, A., Daubechies, I., and Plonka, G. (1997). Regularity of refinable function vectors, J. Fourier Anal. Appl., 3, 295-324.
3. Colella, D. and Heil, C. (1994). Characterizations of scaling functions: Continuous solutions, SIAM J. Matrix Anal. Appl., 15, 496-518.
4. Daubechies, I. and Lagarias, J. (1992). Two-scale difference equations: II. Local regularity, infinite products of matrices, and fractals, SIAM J. Math. Anal., 23, 1031-1079.
5. Deslauriers, G. and Dubuc, S. (1989). Symmetric iterative interpolation processes, Constr. Approx., 5, 49-68.
6. DeVore, R.A. and Lorentz, G.G. (1993). Constructive Approximation, Springer-Verlag, Berlin.
7. Eirola, T. (1992). Sobolev characterization of solutions of dilation equations, SIAM J. Math. Anal., 23, 1015-1030.
8. Goodman, T.N.T., Micchelli, C.A., and Ward, J.D. (1994). Spectral radius formulas for subdivision operators, in Recent Advances in Wavelet Analysis, Schumaker, L.L. and Webb, G., Eds., Academic Press, 335-360.
9. Han, B. and Jia, R.Q. (1998). Multivariate refinement equations and convergence of subdivision schemes, SIAM J. Math. Anal., 29, 1177-1199.
10. Heil, C. and Colella, D. (1994). Dilation equations and the smoothness of compactly supported wavelets, in Wavelets: Mathematics and Applications, Benedetto, J.J. and Frazier, M.W. Eds., CRC Press, Boca Raton, FL, 163-201.
11. Heil, C. and Colella, D. (1996). Matrix refinement equations: existence and uniqueness, J. Fourier Anal. Appl., 2, 363-377.
12. Hogan, T.A. (1997). Stability and linear independence of the shifts of finitely many refinable functions, J. Fourier Anal Appl., 3, 757-774.
13. p spaces, Advances in Comp. Math., 3, 309-341.
14. Jia, R.Q. and Micchelli, C.A. (1992). On linear independence of integer translates of a finite number of functions, Proc. Edinburgh Math. Soc., 36, 69-85.
15. Jia, R.Q., Riemenschneider, S.D., and Zhou, D.X. (1997). Approximation by multiple refinable functions, Canadian J. Math., 49, 944-962.
16. Jia, R.Q., Riemenschneider, S.D., and Zhou, D.X. (1998). Vector subdivision schemes and multiple wavelets, Math. Comp., 67, 1533-1563.
17. Jia, R.Q., Riemenschneider, S.D., and Zhou, D.X. (1999). Smoothness of multiple refinable functions and multiple wavelets, SIAM J. Matrix Anal. Appl., 21, 1-28.
18. Jia, R.Q. and Wang, J.Z. (1993). Stability and linear independence associated with wavelet decompositions, Proc. Am. Math. Soc., 117, 1115-1124.
19. Jia, R.Q. and Zhang, S.R. (1999). Spectral properties of the transition operator associated to a multivariate refinement equation, Linear Algebra and its Applications, 292, 155-178.
20. Jiang, Q.T. and Shen, Z.W. (1999). On existence and weak stability of matrix refinable functions, Constr. Approx., 15, 337-353.
21. p-scaling functions, Asian J. Math., 1, 272-292.
22. 2-scaling functions, SIAM J. Math. Anal., 27, 835-864.
23. p-solutions for the two-scale dilation equations, SIAM J. Math. Anal, 26, 1018-1046.
24. Micchelli, C.A. and Prautzsch, H. (1989). Uniform refinement of curves, Linear Algebra and its Applications, 114/115, 841-870.
25. Rota, G.-C. and Strang, G. (1960). A note on the joint spectral radius, Indag. Math., 22, 379-381.
26. Villemoes, L.F. (1994). Wavelet analysis of refinement equations, SIAM J. Math. Anal., 25, 1433-1460.
27. Wang, J.Z. (1998). Stability and linear independence associated with scaling vectors, SIAM J. Math. Anal., 29, 1140-1156.
28. Wang, Y. (1995). Two-scale dilation equations and the cascade algorithm, Random Comput. Dynamics, 3, 289-307.
29. Wang, Y. (1996). Two-scale dilation equations and mean spectral radius, Random Comput. Dynamics, 4, 49-72.
30. Zhou, D.X. (1997). Existence of multiple refinable distributions, Michigan Math. J., 44, 317-329.
31. Zhou, D.X. (1998). The p-norm joint spectral radius for even integers, Methods and Applications of Analysis, 5, 39-54.