Abstract
In this paper we want to extend the results of pointwise analysis through wavelet transforms to the class of functions where the local fluctuation is bounded by any submultiplicative function. This generalizez the results obtained before in the well-known case of Hölder regularity.
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References
E. M. Stein,Singular Integrals and Differentiability Properties of Functions (Princeton University Press, Princeton, New Jersey, 1970).
S. Jaffard, Estimations Holderiennes ponctuelles des fonctions au moyen de leyrs coefficients d'ondelettes,C. R. Acad. Sci. Ser. I 308:7 (1989).
M. Holschneider and P. Tchamitchihan, Pointwise regularity of Riemanns “nowhere differentiable” function,Inventiones Mathematicae 105:157–175 (1991).
Y. Meyer,Ondelettes et Opérateurs (Hermann, Paris, 1990).
J. M. Combes, A. Grossmann, and P. Tchamitchian. eds.,Wavelets (Springer-Verlag, Berlin, 1989).
I. Daubechies,Ten Lectures on Wavelets (CBMS-NSF Lecture Notes 61, SIAM, Philadelphia, 1992).
M. Holschneider, On the wavelet transformation of fractal objects,J. Stat. Phys. 50:953–993 (1988).
A. Arnéodo, G. Grasseau, and M. Holschneider, On the wavelet transform of multifractals,Phys. Rev. Lett. 61:2281–2284 (1988).
A. Arnéodo, G. Grasseau, and M. Holschneider, Wavelet transform analysis of invariant measures of some dynamical systems, inWavelets, J. M. Combes, A. Grossmann, and P. Tchamitchian, eds. (Springer-Verlag, Berlin, 1989).
A. Grossmann, J. Morlet, and T. Paul, Transforms associated to square integrable group representations I: General results,J. Math. Phys. 26:2473–2479 (1985).
M. Holschneider, Localization properties of wavelet transforms,J. Math. Phys. 34:3227–3244 (1993).
L. Hoermander,The Analysis of Linear Partial Differential Operators (Springer, 1982).
A. Zygmund,Trigonometric Series (Cambridge University Press, Cambridge).
A. Grossmann, M. Holschneider, R. Kronland-Martinet, and J. Morlet, Detection of abrupt changes in sound signals with the help of wavelet transforms, inAdvances in Electronics and Electron Physics, Supplement 19,Inverse Problems (Academic Press, 1987).
M. Holschneider,Wavelets: An Analysis Tool (Oxford University Press, Oxford, to appear).
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Hollschneider, M. More on the analysis of local regularity through wavelets. J Stat Phys 77, 807–840 (1994). https://doi.org/10.1007/BF02179462
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DOI: https://doi.org/10.1007/BF02179462