- 96-245 Charles-Antoine GUERIN and Matthias HOLSCHNEIDER
- Scattering on fractal measures.
(389K, LATEX 209)
Jun 4, 96
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Abstract. We study the one-dimensional potential-scattering problem when the
potential is a Radon measure with compact support. We show that
the usual reflection and transmission amplitude $r(p)$ and $t(p)$ of
an incoming wave $e^{ipx}$ are
well defined. We also show that the
scattering problem on fractal potentials can be obtainded as a limit
case of scattering on smooth potentials. We then explain how to
retrieve the fractal 2-wavelet dimension and/or the correlation
dimension of the potential by mean of
the reflexion amplitude $r(p)$. We study the particular case of
self-similar
measures and show that, under some general conditions, $r(p)$ has a
large scale renormalisation. A numerical application is presented.
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