Spectral Types of Uniform Distribution
Geon Ho Choe · Proceedings of the American Mathematical Society · 1994
We investigate the spectral types of unitary operator $U$ on ${L^2}(\mathbb {T})$ defined by $(Uf)(x) = A(x)f(x + \theta ),|A(x)| = 1$ a.e., where $\mathbb {T}$ is the unit circle identified with the half open interval $[0,1)$ and $\theta$ is irrational. It is shown that Veech’s result on the Kronecker-Weyl theorem modulo $2$ is closely related to the spectral type of $U$.