Fractal Wavelet Dimensions and Time Evolution

Matthias Holschneider

Recherche Coopérative sur Programme n°25 (1994)

  • Volume: 46, page 61-80

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Holschneider, Matthias. "Fractal Wavelet Dimensions and Time Evolution." Recherche Coopérative sur Programme n°25 46 (1994): 61-80. <http://eudml.org/doc/274949>.

@article{Holschneider1994,
author = {Holschneider, Matthias},
journal = {Recherche Coopérative sur Programme n°25},
keywords = {fractal wavelet dimensions; wavelet transforms; correlation dimensions; RAGE theorem},
language = {eng},
pages = {61-80},
publisher = {Institut de Recherche Mathématique Avancée - Université Louis Pasteur},
title = {Fractal Wavelet Dimensions and Time Evolution},
url = {http://eudml.org/doc/274949},
volume = {46},
year = {1994},
}

TY - JOUR
AU - Holschneider, Matthias
TI - Fractal Wavelet Dimensions and Time Evolution
JO - Recherche Coopérative sur Programme n°25
PY - 1994
PB - Institut de Recherche Mathématique Avancée - Université Louis Pasteur
VL - 46
SP - 61
EP - 80
LA - eng
KW - fractal wavelet dimensions; wavelet transforms; correlation dimensions; RAGE theorem
UR - http://eudml.org/doc/274949
ER -

References

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  1. 1. Arnéodo A., Grasseau G., Holschneider M. (1988), On the wavelet transform of multifractals, Phys. Rev. Letters61, 2281-2284 MR966830
  2. 2. Avron J. & Simon B. (1981), Transient and Recurrent Spectrum, Journ. of Funct. Anal.43, 1 Zbl0488.47021MR639794
  3. 3. Combes, J. M., Grossmann A. et Tchamitchian P. Editors, (1989), Wavelets, Springer-VerlagBerlin MR1010895
  4. 4. Cycon H. L., Froese R. G., Kirsch W., Simon B. (1987), Schrödinger Operators, Springer Verlag Zbl0619.47005MR883643
  5. 5. Grossmann A., Morlet J., Paul T. (1986), Transforms associated to square integrable group representations II: examplesAnn. Inst. Henri Poincar, Physique thorique, 45293-309 Zbl0601.22001MR868528
  6. 6. Guarneri I., On an Estimate concerning Quantum Diffusion in the Presence of a Fractal Spectrum, to appear in Europhys. Lett. Zbl0817.47078
  7. 7. Hentschel H. G. E., Procaccia I. (1983), The infinite number of Generalized Dimensions of fractals and strange attractors, Physica8D, 435-444 Zbl0538.58026MR719636
  8. 8. Holschneider M. (1988), On the wavelet transformation of fractal objectsJ. Stat. Phys., 50953-993 Zbl1084.42518MR951066
  9. 9. Holschneider M. (1988), L'analyse d'objets fractals et leur transforme en ondelettesThse de doctorat, Universit de Provence (Aix-Marseille I) 
  10. 10. Holschneider M. (1993), Localization properites of wavelet transforms; Journ. Math. Phys.34 (7), 1993, p. 3227-3244 Zbl0778.42027MR1224209
  11. 11. Holschneider M. (1993), More on the analysis of local regularity through wavelet transforms ; submitted to Journ. Stat. Phys. Zbl0870.42009
  12. 12. Holschneider M., (1994), Functional Calculus using Wavelet Transforms, J. Math. Phys. (to appear) Zbl0824.44005MR1279336
  13. 13. Holschneider M., Tchamitchian Ph. (1991), Pointwise Regularity of Riemanns "nowhere differentiable" function, Inventiones Mathematicae, 105, 157-175 Zbl0741.26004MR1109624
  14. 14. Jaffard S. (1989), Estimations Hlderiennes ponctuelles des fonctions au moyen de leurs coefficients d'ondelettesCRAS Sèr. I308, 7 MR984903
  15. 15. Ketzmerick R., Petschel G., Geisel T., Slow Decay for Temporal Correlations in Quantum Systems with Cantor Spectra, Preprint Univ. Prankfurt Zbl0900.82111
  16. 16. Meyer Y. (1990), Ondelettes et Opèrateurs I&II&III, Hermann, Paris Zbl0694.41037MR1085487
  17. 17. Muzy J. F., Bacry E., Arneodo A., Wavelets and Multifractal Formalism for Singular Signals, Phys. Rev. Lett67, (1992), 3515-3518 
  18. 18. Strichartz R. (1990), Fourier asymptotics of fractal measures, Jour. Funct. Anal., 89, 154 Zbl0693.28005MR1040961

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