On asymptotically almost periodic solutions of a convolution equation

Author:
Olof J. Staffans

Journal:
Trans. Amer. Math. Soc. **266** (1981), 603-616

MSC:
Primary 46F10; Secondary 42A75, 45A05

MathSciNet review:
617554

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Abstract: We study questions related to asymptotic almost periodicity of solutions of the linear convolution equation . Here is a complex measure, and and are bounded functions. Basically we are interested in conditions which imply that bounded solutions of are asymptotically almost periodic. In particular, we show that a certain necessary condition on for this to happen is also sufficient, thereby strengthening earlier results. We also include a result on existence of bounded solutions, and indicate a generalization to a distribution equation.

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DOI:
https://doi.org/10.1090/S0002-9947-1981-0617554-5

Article copyright:
© Copyright 1981
American Mathematical Society