On asymptotically almost periodic solutions of a convolution equation
Author:
Olof J. Staffans
Journal:
Trans. Amer. Math. Soc. 266 (1981), 603616
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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 Y. Katznelson, An introduction to harmonic analysis, Wiley, New York, 1968. MR 0248482 (40:1734)
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 L. H. Loomis, The spectral characterization of a class of almost periodic functions, Ann. of Math. (2) 72 (1960), 362368. MR 0120502 (22:11255)
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 H. Pollard, The harmonic analysis of bounded functions, Duke Math. J. 20 (1953), 499512. MR 0057363 (15:215f)
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 , On the asymptotic spectra of the bounded solutions of a nonlinear Volterra equation, J. Differential Equations 24 (1977), 365382. MR 0463855 (57:3794)
 [15]
 , An asymptotic problem for a positive definite opertorvalued Volterra kernel, SIAM J. Math. Anal. 9 (1978), 855866. MR 506767 (80b:45003)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198106175545
PII:
S 00029947(1981)06175545
Article copyright:
© Copyright 1981
American Mathematical Society
