Almost Periodic Solutions of First- and Second-Order Cauchy Problems
نویسندگان
چکیده
Almost periodicity of solutions of firstand second-order Cauchy problems on the real line is proved under the assumption that the imaginary (resp. real) spectrum of the underlying operator is countable. Related results have been obtained by Ruess Vu~ and Basit. Our proof uses a new idea. It is based on a factorisation method which also gives a short proof (of the vector-valued version) of Loomis' classical theorem, saying that a bounded uniformly continuous function from R into a Banach space X with countable spectrum is almost periodic if c0 /3 X. Our method can also be used for solutions on the half-line. This is done in a separate paper. 1997 Academic Press
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