Random wavelet series

Communications in Mathematical Physics

Volumn 227, Issue 3, 2002, Pages 483-514

  Aubry, Jean Marie ^a   Jaffard, Stéphane ^a  

^a UNIVERSITÉ PARIS EST CRÉTEIL   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035998067     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200200630     Document Type: Article

References (31)

1. Arneodo, A., Bacry, E., Jaffard, S., Muzy, J.-F.: Singularity spectrum of multifractal functions involving oscillating singularities. J. Fourier Anal. Appl. 4 (2), 159-174 (1998)
2. Arneodo, A., Bacry, Muzy, J.-F.: Random cascades on wavelet dyadic trees. J. Math. Phys. 39 (8), 4142-4164 (1998)
3. Aubry, J.-M.: Representation of the singularities of a function. Appl. Comput. Harmonic Anal. 6, 282-286 (1999)
4. Aubry, J. M., Jaffard, S.: Random wavelet series: Theory and applications. To be presented at Fractal 2002, Granada
5. Chillà, F., Peinke, J., Castaing, B.: Multiplicative process in turbulent velocity statistics: A simplified analysis. J. Phys. II France 6 (4), 455-460 (1996)
6. Daubechies, I.: Ten Lectures on Wavelets, Volume 61 of CBMS-NSF regional conference series in applied mathematics. SIAM, 1992
7. Falconer, K.J.: Fractal Geometry: Mathematical Foundations and Applications. Chichester: John Wiley & Sons, 1990
8. Falconer, K.J.: Sets with large intersection properties. J. Lond. Math. Soc. (2) 49, 267-280 (1994)
9. Frisch, U.: Fully developed turbulence and intermittency. In M. Ghil, ed., Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics, Volume 88, International School of Physics Enrico Fermi, Amsterdam: North-Holland, June 1983, pp. 71-88
10. Frisch, U.: Turbulence: The legacy of A.N. Kolmogorov. Cambridge: Cambridge University Press, 1995
11. Jaffard, S.: Multifractal formalism for functions Part I: Resalts valid for all functions. SIAM J. Math. Anal, 28(4), 944-970 (1997)
12. Jaffard, S.: Multifractal formalism for functions Part II: Selfsimilar functions. SIAM J. Math. Anal. 28 (4), 971-998 (1997)
13. Jaffard, S.: Oscillation spaces: Properties and applications to fractal and multifracal functions. J. Math. Phys. 39 (8), 4129-4141 (1998)
14. Jaffard, S.: Lacunary wavelet series. Ann. Appl. Probab. 10 (1), 313-329 (2000)
15. Jaffard, S.: On the Frish-Parisi conjecture. J. Math. Pures Appl. 79 (6), 525-552 (2000)
16. Jaffard, S.. Meyer, Y.: Wavelet methods for pointwise regularity and local oscillations of functions. Mem. Amer. Math. Soc. 123, 587 (Sept. 1996)
17. Jaffard, S., Meyer, Y.: On the pointwise regularity of functions in critical Besov spaces. J. Funct. Anal. 175, 415-434 (2000)
18. Kahane, J.-P.: Some random series of functions. Cambridge: Cambridge University Press, 1985
19. Kolmogorov, A. N.: C. R. Acad. Sci. URSS 30, 301-305 (1941)
20. Kolmogorov, A. N.: J. Fluid Mech. 13, 82-85 (1962)
21. Körner, T.: Kahane's Helson curve. J. Fourier Anal. Appl., pp. 325-346 (1995). Special Issue: Proceedings of the conference in honor of J.-P. Kahane
22. Lemarié, P.-G., Meyer, Y.: Ondelettes et bases hilbertiennes. Rev. Mat. Iber. 2 (1/2), 1-18 (1987)
23. Mandelbrot, B. B.: Intermittent turbulence in self similar cascades: Divergence of high moments and dimension of the carrier. J. Fluid Mech. 62, 331-358 (1974)
24. Mattila, P.: Geometry of Sets and Measures in Euclidean Spaces, Volume 44 of Cambridge studies in advanced mathematics. Cambridge: Cambridge University Press, 1995
25. Meneveau, C., Sreenivasan, K.: Measurement of f(α) from scaling of histograms and applications to dynamical systems and fully developed turbulence. Phys. Letters A 137, 103-112 (1989)
26. Meyer, Y.: Ondelettes et Opérateurs I: Ondelettes. Actualités Mathématiques. Paris: Hermann. 1990
27. Müller, P., Vidakovic, B. (editors): Bayesian Inference in Wavelet Based Models, Volume 141 of Lect. Notes Stat., Berlin-Heidelberg-New York: Springer-Verlag, 1999
28. Shepp, L.A.: Covering the circle with random arcs. Israel J. Math. 11, 328-345 (1972)
29. Simoncelli, E.: Bayesian denoising of visual images in the wavelet domain. Lect. Notes Stat. 141, 291-308 (1999)
30. Stute, W.: The oscillation behavior of empirical processes. Ann. Probab. 10, 86-107 (1982)
31. Tricot, C.: Two definitions of fractional dimension. Math. Proc. Cambridge Philos. Soc. 91, 57-74 (1982)