On the existence of the ergodic Hilbert transform
The main result of the paper is the equivalence between the existence of ergodic Hilbert transform and the ergodic average in the sense of almost sure convergence for a unitary operator in \(L_ 2\). To prove this result the author uses the spectral representation of this operator.
ergodic average in the sense of almost sure convergence for a unitary operator in \(L_ 2\)
scientific article; zbMATH DE number 4032414