Xing-Gang He

Spectral eigenvalue problem of Cantor measures and Artin's primitive root conjecture

The eigenvalue problem for a probability measure $\mu$ with compact support in $\R$ is whether there exist a countable set $\Lambda$ and a nonzero real $t\ne 1$ such that both $\Lambda$ and $t\Lambda$ are spectra of $\mu$, that is, the family $$E_{a\Lambda}=\{e^{-2\pi i a\lambda x}:\lambda\in\Lambda\}$$ is an orthonorm...