### Almost-periodic mild solutions to a class of partial functional-differential equations.

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We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form ẋ = A(t)x + f(t) (*), with f having precompact range, which is then applied to find new spectral criteria for the existence of almost periodic solutions with specific spectral properties in the resonant case where $\overline{{e}^{isp\left(f\right)}}$ may intersect the spectrum of the monodromy operator P of (*) (here sp(f) denotes the Carleman spectrum of f). We show that if (*) has a bounded...

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