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A Tauberian problem for a Volterra integral operator

Author: Gustaf Gripenberg
Journal: Proc. Amer. Math. Soc. 82 (1981), 576-582
MSC: Primary 45D05; Secondary 40E05
MathSciNet review: 614881
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Abstract: The following question is studied: For which (nonintegrable) kernels $ A$ does $ {\lim _{t \to \infty }}\int _0^tA(t - s)x(s)ds = 0$ imply that $ {\lim _{t \to \infty }}x(t) = 0$ when $ x$ is bounded and satisfies a Tauberian condition.

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Article copyright: © Copyright 1981 American Mathematical Society

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