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Transactions of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9947-1981-0617554-5
MathSciNet review: 617554
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Abstract: We study questions related to asymptotic almost periodicity of solutions of the linear convolution equation $ ( \ast )\mu \ast x = f$. Here $ \mu $ is a complex measure, and $ x$ and $ f$ are bounded functions. Basically we are interested in conditions which imply that bounded solutions of $ ( \ast )$ are asymptotically almost periodic. In particular, we show that a certain necessary condition on $ f$ 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

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