Intertwining multiresolution analyses and the construction of piecewise-polynomial wavelets

SIAM Journal on Mathematical Analysis

Volumn 27, Issue 6, 1996, Pages 1791-1815

  Donovan, George C ^a   Geronimo, Jeffrey S ^a   Hardin, Douglas P ^b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b VANDERBILT UNIVERSITY   (United States)

Author keywords

Intertwining multiresolution analyses; Multiwavelet; Orthogonal wavelet; Splines

Indexed keywords

EID: 0040745989     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141094276160     Document Type: Article

References (23)

1. G. BATTLE, A block spin construction of ondelettes, part I: Lemarié functions, Comm. Math. Phys., 110 (1987), pp. 601-615.
2. d), J. Funct. Anal., 119 (1994), pp. 37-78.
3. _, On the construction of multivariate (pre)wavelets, Constr. Approx., 9 (1993), pp. 123-166.
4. C. K. CHUI AND J. Z. WANG, A cardinal spline approach to wavelets, Proc. Amer. Math. Soc., 113 (1991), pp. 785-793.
5. I. DAUBECHIES, Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, Philadelphia, 1992.
6. S. DEMKO, W. F. Moss, AND P. W. SMITH, Decay rates for inverses of banded matrices, Math. Comp., 43 (1984), pp. 491-499.
7. G. C. DONOVAN, J. S. GERONIMO, D. P. HARDIN, AND P. R. MASSOPUST, Construction of orthogonal wavelets using fractal interpolation functions, SIAM J. Math. Analysis, 27 (1996), pp. 1158-1192.
8. 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), pp. 373-401.
9. J. S. GERONIMO, E. M. HARRELL II, AND W. VAN ASSCHE, On the asymptotic distribution of eigenvalues of banded matrices, Const. Approx., 4 (1988), pp. 403-417.
10. T. N. T. GOODMAN, S. L. LEE, AND W. S. TANG, Wavelets in wandering subspaces, Trans. Amer. Math. Soc., 338 (1993), pp. 639-654.
11. T. N. T. GOODMAN AND S. L. LEE, Wavelets of multiplicity r, Trans. Amer. Math. Soc., to appear.
12. D. P. HARDIN, B. KESSLER, AND P. R. MASSOPUST, Multiresolution analyses and fractal functions, J. Approx. Theory, 71 (1992), pp. 104-120.
13. L. HERVÈ, Multi-resolution analysis of multiplicity d: Application to dyadic interpolation, Comput. Harmonic Anal., 1 (1994), pp. 299-315.
14. R. JIA AND C. A. MICCHELLI, Using the refinement equation for the construction of pre-wavelets II: Powers of two, in Curves and Surfaces, P. J. Laurent, A. le Méhauté, and L. L. Shumaker, eds., Academic Press, New York, 1991, pp. 209-246.
15. R. JIA AND Z. SHEN, Multiresolution and wavelets, Proc. Edinburgh Math. Soc., 37 (1994), pp. 271-300.
16. W. LAWTON, S. L. LEE, AND Z. SHEN, An algorithm for matrix extension and wavelet construction, Math. Comp., to appear.
17. n), J. Math. Pures Appl., 67 (1988), pp. 227-236.
18. C. MICCHELLI, Using the refinement equation for the construction of pre-wavelets VI: Shift invariant subspaces, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 356 (1992), pp. 213-222.
19. M. REED AND B. SIMON, Functional Analysis, Academic Press, New York, 1980.
20. A. RON, Factorization theorems of univariate splines on regular grids, Israel J. Math., 70 (1990), pp. 48-68.
21. L. L. SCHUMAKER, Spline Functions: Basic Theory, John Wiley, New York, 1981.
22. G. STRANG AND V. STRELA, Short wavelets and matrix dilation equations, IEEE Trans. SP, 43 (1995), pp. 108-115.
23. P. P. VAIDYANATHAN, Multirate Systems and Filter Banks, Simon and Schuster, New York, 1993.