Multidimensional periodic multiwavelets

Journal of Approximation Theory

Volumn 98, Issue 1, 1999, Pages 72-103

  Goh, Say Song ^a   Lee, S L ^a   Teo, K M ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

infinite matrix product; matrix extension; multidimensional periodic multiwavelets; Periodic multiresolution with multiplicityrand dilation matrixM

Indexed keywords

EID: 0033130210     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.1998.3279     Document Type: Article

References (29)

1. de Boor C., DeVore R., Ron A. On the construction of multivariate (pre)wavelets. Constr. Approx. 9:1993;123-166.
2. Chen H. L. Antiperiodic wavelets. J. Comput. Math. 14:1996;32-39.
3. Chen H. L. Wavelets from trigonometric spline approach. J. Approx. Theory Appl. 12:1996;99-110.
4. Chen H. L. Construction of orthonormal wavelets in the periodic case. Chinese Sci. Bull. 14:1996;552-554.
5. Chen H. L. Wavelets on the unit circle. Results Math. 31:1997;322-336.
6. Chen H. L., Jin G. R., Liang X. Z. Bivariate box-spline wavelets (periodic). Chen M. T. Harmonic Analysis in China. 1995;Kluwer Academic, Dordrecht/Norwell.
7. Chui C. K., Lian J. A study on orthonormal multi-wavelets. Appl. Numer. Math. 20:1996;273-298.
8. Chui C. K., Mhaskar N. H. On trigonometric wavelets. Constr. Approx. 9:1993;167-190.
9. Cohen A., Daubechies I., Plonka G. Regularity of refinable function vectors. J. Fourier Anal. Appl. 3:1997;295-324.
10. Dahmen W., Micchelli C. A. Biorthogonal wavelet expansions. Constr. Approx. 13:1997;293-328.
11. Davis P. J. Circulant Matrices. 1979;Wiley, New York.
12. Goodman T. N. T. Construction of wavelets with multiplicity. Rend. Mat. Ser. VII. 15:1994;665-691.
13. T. N. T. Goodman, S. L. Lee, Convergence of nonstationary vector cascade algorithms, Num. Math.
14. Heil C., Colella D. Matrix refinement equations: existence and uniqueness. J. Fourier Anal. Appl. 2:1996;363-377.
15. Heil C., Strang G., Strela V. Approximation by translates of refinable functions. Numer. Math. 73:1996;75-94.
16. Jacobson N. Basic Algebra, I. 1985;Freeman, New York.
17. Q. Jiang, Z. Shen, On the existence and weak stability of matrix refinable functions, Constr. Approx.
18. Koh Y. W., Lee S. L., Tan H. H. Periodic orthogonal splines and wavelets. Appl. Comput. Harmon. Anal. 2:1995;201-218.
19. Lawton W., Lee S. L., Shen Z. An algorithm for matrix extension and wavelet construction. Math. Comp. 65:1996;723-737.
20. Lian J. A. Characterization of the order of polynomial reproduction for multiscaling functions. CAT Report. 1995.
21. Meyer Y. Wavelets and Operators. 1993;Cambridge Univ. Press, Cambridge.
22. Micchelli C. A., Sauer T. Regularity of multiwavelets. Adv. Comput. Math. 7:1997;455-545.
23. Narcowich F. J., Ward J. D. Wavelets associated with periodic basis functions. Appl. Comput. Harmon. Anal. 3:1996;40-56.
24. Perrier V., Basdevant C. Periodic wavelet analysis, a tool for inhomogeneous field investigation. Theory and algorithms. Rech. Aérospat. 3:1989;53-67.
25. Plonka G., Tasche M. A unified approach to periodic wavelets. Chui C. K., Montefusco L., Puccio L. Wavelet Analysis and Its Applications. 1994;137-151 Academic Press, San Diego.
26. Plonka G., Tasche M. On the computation of periodic spline wavelets. Appl. Comput. Harmon. Anal. 2:1995;1-14.
27. Shen Z. Refinable function vectors. SIAM J. Math. Anal. 29:1998;235-250.
28. F. Sprengel, Periodic interpolation on sparse grid, 1996.
29. Strang G., Strela V. Short wavelets and matrix dilation equations. IEEE Trans. Signal Process. 43:1995;108-115.