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

Jordan, G. S.; Wheeler, Robert L.

doi:10.1090/S0002-9939-1976-0405023-0

A generalization of the Wiener-Lévy theorem applicable to some Volterra equations
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by G. S. Jordan and Robert L. Wheeler

Proc. Amer. Math. Soc. 57 (1976), 109-114

DOI: https://doi.org/10.1090/S0002-9939-1976-0405023-0

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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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