Regular stationary stochastic vector processes whose spectral densities are the boundary values of matrix functions with bounded Nevanlinna characteristic are considered. A criterion for the representability of such processes as output data of linear time invariant dynamical systems is established.
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Let w be a non-negative measurable function defined on the positive semi-axis and satisfying the reverse Hölder inequality with exponents 0 < α < β. In the present paper, sharp estimates of the compositions of the power means $𝓟_{α}w(x): = ((1/x) ∫_{0}^{x} w^{α}(t)dt)^{1/α}$, x > 0, are obtained for various exponents α. As a result, for the function w a property of self-improvement of summability exponents is established.
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