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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Two Tauberian theorems for nonconvolution Volterra integral operators


Author: Gustaf Gripenberg
Journal: Proc. Amer. Math. Soc. 89 (1983), 219-225
MSC: Primary 45D05; Secondary 40E05
MathSciNet review: 712626
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Abstract: Two sets of sufficient conditions on the kernel $ k(t,s)$ are given so that one can prove that if $ x$ is a bounded function such that

$\displaystyle \mathop {\lim }\limits_{\begin{array}{*{20}{c}} {t \to \infty } \... ...text{and}}\quad \mathop {\lim }\limits_{t \to \infty } \int_0^t {k(t,s)x(s)ds} $

exists, then $ {\lim _{t \to \infty }}x(t)$ exists.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0712626-6
PII: S 0002-9939(1983)0712626-6
Article copyright: © Copyright 1983 American Mathematical Society