Функциональные модели несамосопряженных операторов, сильно непрерывные полугруппы и матричные веса Макенхаупта

We consider unbounded continuously invertible operators A, A0 on a Hilbert space H such that the operator A −1 − A−1 0 has finite rank. Assuming that σ(A0) = ∅ and the semigroup V+(t) := exp{iA0t}, t > 0, is of class C0, we state criteria under which the semigroups U±(t) := exp{±iAt}, t > 0, are also of class C0. We give applications to the theory of mean-periodic functions. The investigation is based on functional models of non-selfadjoint operators and on the technique of matrix Muckenhoupt weights.