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.
