Let L be an arbitrary linear partial differential operator and let f be an almost periodic function for t in Rm. In this paper we present sufficient conditions that a bounded solution u of Lu = f be almost periodic. Our work generalizes the theorem of Sibuya  for Poisson's equation and the theorems of Favard  and Bochner  for ordinary differential equations.
Bibliographical noteFunding Information:
* This work was done while the author was visiting the Istituto Matematico dell’Universit8 di Firenze under the auspices of the Italian Research Council (C.N.R.). Partial support for this research was also given by NSF Grant No. GP-27275.
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