Toward discrete wavelets with irrational scaling factor

Journal of Mathematical Physics

Volumn 37, Issue 6, 1996, Pages 3001-3013

  Gazeau, Jean Pierre ^a   Spiridonov, Vyacheslav ^b,c  

^a UNIVERSITÉ PARIS DESCARTES   (France)

^b UNIVERSITÉ DE MONTRÉAL   (Canada)

^c INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030558511     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531551     Document Type: Article

References (17)

1. Y. Meyer, Ondelettes et Opérateurs I (Hermann, Paris, 1990); Wavelets. Algorithms and Applications (SIAM, Philadelphia, 1993).
2. Y. Meyer, Ondelettes et Opérateurs I (Hermann, Paris, 1990); Wavelets. Algorithms and Applications (SIAM, Philadelphia, 1993).
3. I. Daubechies, Ten Lectures on Wavelets (SIAM, Philadelphia, 1992).
4. 2(R) with rational dilation factor," in Wavelets and Their Applications, edited by M. B. Ruskai et al. (Jones and Bartlett, Boston, 1992). pp. 439-452.
5. P. Guyot, P. Kramer, and M. de Boissieu, "Quasicrystals," Rep. Prog. Phys. 54, 1373-1425 (1991).
6. M. J. Bertin, A. Decomps-Guilloux, M. Grandet-Hugot, M. Pathiaux-Delefosse, and J. P. Schreiber, Pisot and Salem Numbers (Birkhäuser Verlag, Basel, 1992).
7. V. Spiridonov, "Universal superpositions of coherent states and self-similar potentials," Phys. Rev. A 52, 1909-1935 (1995).
8. J. P. Gazeau and J. Patera, "Tau-wavelets of Haar," J. Phys. A (to be published).
9. P. Janardhan, D. Rosenblum, and R. S. Strichartz, "Numerical experiments in Fourier asymptotics of Cantor measures and wavelets," Exp. Math. 1, 249-273 (1992).
10. A. Rényi, "Representations for real numbers and their ergodic properties," Acta Math. Acad. Sci. Hungary 8 (3-4), 477-493 (1957).
11. A. Bertrand, "Développements en base de Pisot et répartition modulo 1," C. R. Acad Sci. Paris 285, 419-421 (1977).
12. S. Dubuc, "Interpolation fractale," in Fractal Geometry and Analysis, NATO ASI Series, Vol. C346, edited by J. Bélair and S. Dubuc (Kluwer Academic, New York, 1991), pp. 121-220.
13. n," IEEE Trans. Inf. Theory 38, 556-568 (1992).
14. A. S. Cavaretta, W. Dahmen, and C. A. Micchelli, "Stationary subdivision," Mem. Am. Math. Soc. 93, 1-186 (1991).
15. n," in Fourier Analysis: Analytic and Geometric Aspects, Lecture Notes in Pure and Applied Mathemathics (1994), Vol. 157, pp. 187-196.
16. Y. Meyer, "Quasicrystals, Diophantine approximation and algebraic numbers," in Beyond Quasicrystals, Proceedings of the 1994 Les Mouches Winter School, edited by F. Axel and D. Gratias (Springer-Verlag, Berlin, 1995), pp. 3-16.
17. Č. Burdík, Ch. Frougny, J. P. Gazeau, and E. Pelantová, "τ-integers and five-fold Meyer sets in the plane," preprint DOPP-MF-95/1, 1995.