Spectra of deranged Cantor set by weak local dimensions

Abstract

We decompose the most generalized Cantor set into a spectral class using weak lower (upper) local dimension. Each member of the spectral class is related to a quasi-self-similar measure, so the information of its Hausdorff (packing) dimension can be obtained. In the end, we give an example of the Cantor set having countable members composing the spectral class.