Characterization on spectra of self-similar measures and the dual spectral set conjecture

Li-Xiang An, Yan-Song Fu, Ming-Xuan Jiang

A discrete set $\Lambda$ is called a {\it spectrum} of a Borel probability measure $\mu$ if the exponential functions $\{e^{2\pi i⟨\lambda ,x⟩}:\lambda \in \Lambda \}$ form an orthonormal basis for $…