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Proceedings of the American Mathematical Society

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

 

 

Linear convolution integral equations with asymptotically almost periodic solutions


Authors: G. S. Jordan, W. R. Madych and R. L. Wheeler
Journal: Proc. Amer. Math. Soc. 78 (1980), 337-341
MSC: Primary 45E10
DOI: https://doi.org/10.1090/S0002-9939-1980-0553371-7
MathSciNet review: 553371
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Abstract: Let $ \mu $ be a bounded Borel measure and f be asymptotically almost periodic. Conditions are found which ensure that certain bounded solutions of the linear convolution integral equation $ g \ast \mu = f$ are asymptotically almost periodic. This result is also extended to the case where the measure $ \mu $ is replaced by a tempered distribution $ \tau $ for which convolution with bounded functions makes sense.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0553371-7
Keywords: Convolution integral equation, asymptotically almost periodic, tempered distribution
Article copyright: © Copyright 1980 American Mathematical Society