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A generalization of the Wiener-Lévy theorem applicable to some Volterra equations

Authors: G. S. Jordan and Robert L. Wheeler
Journal: Proc. Amer. Math. Soc. 57 (1976), 109-114
MSC: Primary 45D05
MathSciNet review: 0405023
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Abstract: Recently, Shea and Wainger obtained a variant of the Wiener-Lévy theorem for nonintegrable functions of the form $ a(t) = b(t) + \beta (t)$, where $ b(t)$ is nonnegative, nonincreasing, convex and locally integrable, and $ \beta (t),t\beta (t) \in {L^1}(0,\infty )$. It is shown here that the moment condition $ t\beta (t) \in {L^1}$ may be omitted from the hypotheses of this theorem. These results are useful in the study of stability problems for some Volterra integral and integrodifferential equations.

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Keywords: Volterra equations, resolvent, Fourier transform, Laplace transform
Article copyright: © Copyright 1976 American Mathematical Society

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