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Proceedings of the American Mathematical Society

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Almost periodic solutions of Poisson's equation


Author: Yasutaka Sibuya
Journal: Proc. Amer. Math. Soc. 28 (1971), 195-198
MSC: Primary 35.75
MathSciNet review: 0285816
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Abstract: It is well known that if $ f(t)$ is almost periodic with respect to a real variable $ t$, and if $ F(t) = {\smallint ^t}f(s)ds$ is bounded for $ - \infty < t < \infty $, then $ F(t)$ is also almost periodic in $ t$. We shall prove a similar result for Poisson's equation.


References [Enhancements On Off] (What's this?)

  • [1] R. Courant, Methods of mathematical physics. Vol. II: Partial differential equations, Interscience, New York, 1962. MR 25 #4216.
  • [2] J. Favard, Leçons sur les fonctions presque-périodiques, Gauthier-Villars, Paris, 1933.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0285816-9
Keywords: Poisson's equation, bounded generalized solutions, almost periodicity in $ {R^m}$, almost periodic solutions
Article copyright: © Copyright 1971 American Mathematical Society