Nonstationary subdivision schemes and multiresolution analysis

SIAM Journal on Mathematical Analysis

Volumn 27, Issue 6, 1996, Pages 1745-1769

  Cohen, Albert ^a   Dyn, Nira ^b  

^a SORBONNE UNIVERSITÉ   (France)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

Dyadic interpolation; Multiresolution analysis; Spectral approximation; Subdivision schemes; Wavelets

Indexed keywords

EID: 0030490346     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S003614109427429X     Document Type: Article

References (23)

1. S. BERKOLAIKO AND I. NOVIKOV (1992), Sur des presque-ondelettes indéfiniment différentiables à support compact, Dokl. Acad. Nauk., 326, pp. 935-938.
2. A. CAVARETTA, W. DAHMEN, AND C. A. MICCHELLI (1991), Stationary subdivision, Mem. Amer. Math. Soc., 93, pp. 1-186.
3. A. COHEN, I. DAUBECHIES, AND P. VIAL (1993), Wavelets and fast wavelet transforms on an interval, Appl. Comput. Harmonic Anal., 1, pp. 54-81.
4. W. DAHMEN AND A. KUNOTH (1992), Multilevel preconditioning, Numer. Math., 63, pp. 315-345.
5. I. DAUBECHIES (1988), Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math., 41, pp. 909-996.
6. _ (1992), Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, Philadelphia.
7. I. DAUBECHIES AND J. LAGARIAS (1991), Two scale difference equations I: Existence and global regularity of solutions, SIAM J. Math. Anal., 22, pp. 1388-1410.
8. d), Report CMS TSR 92-2, University of Wisconsin, Madison, WI.
9. G. DERFEL, N. DYN, AND D. LEVIN (1995), Generalized functional equations and subdivision processes, J. Approx. Theory, 80, pp. 272-297.
10. G. DESLAURIERS AND S. DUBUC (1987), Interpolation dyadique, in Fractals, Dimensions Non Entières et Applications, G. Cherbit, ed., Masson, Paris, pp. 44-55.
11. N. DYN (1992), Subdivision schemes in computer-aided geometric design, in Advances in Numerical Analysis II: Wavelets, Subdivision Algorithms and Radial Functions, W. A. Light, ed., Oxford University Press, Oxford, UK, pp. 36-104.
12. N. DYN AND D. LEVIN (1990), Interpolating subdivision schemes for the generation of curves and surface, in Multivariate Approximation and Interpolation, W. Haussmann and K. Jetter, eds., Birkhäuser-Verlag, Basel, Switzerland, pp. 91-106.
13. N. DYN, J. A. GREGORY, AND D. LEVIN (1987), A four-point interpolatory subdivision scheme for curve design, Comput. Aided Geom. Design, 4, pp. 257-268.
14. N. DYN AND A. RON (1995), Multiresolution analysis by infinitely differentiate compactly supported functions, Appl. Comput. Harmonic Anal., 2, pp. 15-20.
15. M. FRAZIER AND B. JAWERTH (1985), Decomposition of Besov spaces, Indiana Univ. Math. J., 34, pp. 777-799.
16. L. HORMANDER (1983), The Analysis of Partial Differential Equations, vol. I, Springer-Verlag, Berlin, New York, Heidelberg.
17. S. MANDELBROJT (1942), Analytic functions and classes of infinitely differentiate functions, Rice Inst. Pamphlet, 29, pp. 1-142.
18. Y. MEYER (1990), Ondelettes et Opérateurs, Hermann, Paris.
19. A. RON (1995), Approximation orders of and approximation maps from local principal shift invariant spaces, J. Approx. Theory, 81, pp. 38-65.
20. V. L. RVACHEV AND V. A. RVACHEV (1971), On a function with compact support, Dopov. Dokl. Akad. Nauk. Ukraïni, 8, pp. 705-707 (in Ukrainian).
21. V. A. RVACHEV (1990), Compactly supported solutions of functional-differential equations and their applications, Russian Math. Surveys, 45, pp. 87-120.
22. H. VOLKMER (1992), On the regularity of wavelets, IEEE Trans. Inform. Theory, 38, pp. 872-876.
23. K. ZAO (1995), Simultaneous approximation from PSI spaces, J. Approx. Theory, 81, pp. 166-184.