Almost Periodic Solutions of First-and Second-Order Cauchy Problems

  title={Almost Periodic Solutions of First-and Second-Order Cauchy Problems},
  author={Wolfgang Arendt},
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… CONTINUE READING

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