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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Almost periodic solutions of Poisson’s equation


Author: Yasutaka Sibuya
Journal: Proc. Amer. Math. Soc. 28 (1971), 195-198
MSC: Primary 35.75
DOI: https://doi.org/10.1090/S0002-9939-1971-0285816-9
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?)

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

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Keywords: Poisson’s equation, bounded generalized solutions, almost periodicity in <IMG WIDTH="36" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${R^m}$">, almost periodic solutions
Article copyright: © Copyright 1971 American Mathematical Society