Controlling orthogonal series with irrational rotations (Q1586349)

The paper proposes irrational rotations on the torus as a convenient tool to compute covering numbers for partial sums of orthogonal series. That yields an estimation of entropy numbers for stationary random processes with values in Hilbert space \(L^2([0,1[,\mu)\). Further, the connection with almost sure convergence of a random process is mentioned together with an illustrative counterexample.