Spectral Types of Uniform Distribution

Abstract

Abstract. We investigate the spectral types of unitary operator U on L2 (T) defined by (Uf)(x) = A{x)f{x + 6), \A{x)\ = 1 a.e., where T is the unit circle identified with the half open interval [0,1) and 8 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 .