Fourier Basis and Spectrality of Moran measures with Element Digit Sets

Abstract

We show the classification of the digit sets as product-forms. The spectral property of a class of cantor measures with consecutive digits and on R^*are given . The spectral structure of digit sets of self-similar tiles on R^1 with non-spectral problem for a class of planar self-affine measures in R^Nwith two-element digit set and decomposable digit sets are studied . The Mock Fouier series and existence of orthonormal bases of Certain Cantor-Moran measures are discussed. The spectrality ofa class of infinite convolutions and Cantor Moran measures with three-element digit sets are obtained . The spectrality of Moran measures with four-element digit sets and one dimensional self-similar measures with consecutive digits are in vestigated.