Weighted Fourier Frames and Basis on Self – Affine with Moran and Sum of Singular Measures

Abstract

We show the analysis of orthogonality Fourier frequencies and orbits in affine iterated function systems. We characterize the Fourier frames for the Cantor-4set, of absolutely continuous measures and for singular measures with weighted Fourier frames and Hadamard triples generate self-affine spectral and fractal measures. A class of spectral, divergence of the Mock and Scrambled Fourier analysis on Moran and fractal measures are considered. We determime the spectrality of a class of infinite Bernoulli convolutions and Fourier orthonormal bases and existence for Cantor-Moran measure. The uniformity and translation absolute continuity of measures with Fourier frames and a sum of singular measures are discussed.