Spectral Criteria for Existence ofGeneralized Ergodic Transforms
Владимир Федорович Гапошкин · Theory of Probability and Its Applications · 1997
Conditions are studied for a.e. convergence of one-sided and two-sided ergodic transforms $$ \sum_1^\iy b_kT^kf(x)\q\hbox{and}\q \sum_{-\iy}^\iy b_kT^kf(x), $$ where T is a unitary operator in $L^2$. Criteria for existence of these transforms are obtained in terms of the properties of the operator spectral measure. Similar results are stated for normal operators and for stationary and harmonizable stochastic processes