engleski

Admissibility for exponential dichotomies in average

We characterize completely the notion of an exponential dichotomy in average in terms of an admissibility property. The notion corresponds to a generalization of that of an exponential dichotomy to measurable cocycles acting on $L^1$ functions with respect to a given probability measure. The admissibility property is described in terms of the injectivity and surjectivity of a certain linear operator in the space of bounded sequences of $L^1$ functions. The characterization is then used to establish in a simple manner the robustness of the notion, in the sense that it persists under sufficiently small linear perturbations. We note that we consider both $\Z$-cocycles and $\N$-cocycles.

admissibility ; exponential dichotomies in average ; robustness

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