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On the determination of box dimensions by means of wavelet transforms

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Abstract

Sufficient conditions are established for the determination of box dimensions of graphs from the decrease of the corresponding wavelet transforms. As an application, wavelet Weierstrass functions are constructed.

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References

  1. A. Arneodo, G. Grasseau, and M. Holschneider,Phys. Rev. Lett. 61:2281 (1988).

    Google Scholar 

  2. K. J. Falconer,Fractal Geometry (Wiley, New York, 1990).

    Google Scholar 

  3. J. M. Ghez and S. Vaienti,J. Stat. Phys. 57:415 (1989).

    Google Scholar 

  4. J. M. Ghez and S. Vaienti,Nonlinearity 3:777, 791 (1992).

    Google Scholar 

  5. M. Holschneider,J. Stat. Phys. 50:963 (1988).

    Google Scholar 

  6. M. Holschneider and P. Tchamitchian,Invent. Math. 105:157 (1991).

    Google Scholar 

  7. J. E. Littlewood,Proc. Lond. math. Soc. (2) 5:361 (1907).

    Google Scholar 

  8. Y. Meyer,Ondelettes et Opérateurs, I–III (Hermann, Paris, 1990).

    Google Scholar 

  9. S. Vaienti,Nonlinearity 4:1241 (1991).

    Google Scholar 

  10. K. Weierstrass, über continuirliche Functionen eines reellen Arguments, die für keinen Werth des letzteren einen bestimmten Differentialquotienten besitzen, inMathematische Werke II (Berlin: Mayer & Muller 1895), p. 71.

    Google Scholar 

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Rasmussen, H.O. On the determination of box dimensions by means of wavelet transforms. J Stat Phys 71, 817–823 (1993). https://doi.org/10.1007/BF01058449

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