descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Mar 1980Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 78, page 337 (issn: 0002-9939,

Authors: R. L. Wheeler; G. S. Jordan; W. R. Madych;

doi: 10.2307/2042320 , 10.1090/s0002-9939-1980-0553371-7

Linear Convolution Integral Equations with Asymptotically Almost Periodic Solutions

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Abstract

Let μ \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 ∗ μ = f g \ast \mu = f are asymptotically almost periodic. This result is also extended to the case where the measure μ \mu is replaced by a tempered distribution τ \tau for which convolution with bounded functions makes sense.

Keywords

linear convolution integral equations, asymptotically almost periodic solutions, tempered distribution, Classical almost periodic functions, mean periodic functions, Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), Asymptotics of solutions to integral equations, Operations with distributions and generalized functions

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