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Description:
We consider operator-valued boundary value problems in (0;2π)n with periodic or, more generally, v-periodic boundary conditions. Using the concept of discrete vector-valued Fourier multipliers, we give equivalent conditions for the unique solvability of the boundary value problem. As an application, we study vector-valued parabolic initial boundary value problems in cylindrical domains (0;2π)n x V with v-periodic boundary conditions in the cylindrical directions. We show that under suitable assumptions on the coefficients, we obtain maximal Lq-regularity for such problems. ; published