7,399 research outputs found
Mean sensitive, mean equicontinuous and almost periodic functions for dynamical systems
We show that an -topological dynamical system equipped with an invariant
ergodic measure has discrete spectrum if and only it is -mean
equicontinuous (proven for before). In order to do this we introduce mean
equicontinuity and mean sensitivity with respect to a function. We study this
notion in the topological and measure theoretic setting. In the measure
theoretic case we characterize almost periodic functions and in the topological
case we show that weakly almost periodic functions are mean equicontinuous (the
converse does not hold)
Perturbation of strong Feller semigroups and well-posedness of semilinear stochastic equations on Banach spaces
We prove a Miyadera-Voigt type perturbation theorem for strong Feller
semigroups. Using this result, we prove well-posedness of the semilinear
stochastic equation dX(t) = [AX(t) + F(X(t))]dt + GdW_H(t) on a separable
Banach space E, assuming that F is bounded and measurable and that the
associated linear equation, i.e. the equation with F = 0, is well-posed and its
transition semigroup is strongly Feller and satisfies an appropriate gradient
estimate. We also study existence and uniqueness of invariant measures for the
associated transition semigroup.Comment: Revision based on the referee's comment
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