Fractal sets and their relation with wavelet sets
Ataollah Askari Hemmat
Dept. of Math. Vali Asr University, Rafsanjan, Kerman
IRAN, ISLAMIC REPUBLIC OF
given at strobl07 (21.06.07 15:45)
Sets with non-integeral
Hausdorff dimension are called fractals by Mandelbrot, when they
have the additional property of being in some sense either
strictly or statistically self similar, have been used to model
various physical phenomena. In this article we will review the theory
of wavelet sets and
fractls. In dimension 2 we will prove that under certain conditions
the product of two sets is a wavelet set. This is completely new
and we will present few new examples. We will explain fractal sets and show
how some fractal sets can be obtained from wavelet sets.
Keywords: Fractals, Multiresolution Analysis, Wavelets, Wavelet Sets, Digits.