Abstract
We study the weighted l1 Paley–Wiener Theorem, with applications to stability of the linear multi-step time discretization for a linear Volterra equation of scalar type in a Hilbert space. The results extend to weighted l1 stability some recent l1 stability theorem due to the author (Numer. Math. 109 (2008) 571–595). Our theoretical results are applied to investigate the asymptotic behavior as tn→∞ of the numerical solutions of certain integro-differential equations in Hilbert space.
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