A functional-analytical approach to the asymptotics of recursions

Pötzsche, Christian

doi:10.1090/S0002-9939-09-09360-5

A functional-analytical approach to the asymptotics of recursions
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Proc. Amer. Math. Soc. 137 (2009), 3297-3307 Request permission

Abstract:

We propose a functional-analytical method to investigate the long-term behavior of recursions (difference equations). It is based on a formulation of given (implicit) recursions as abstract operator equations in sequence spaces. Solving them using appropriate tools from nonlinear analysis yields quantitative convergence results and equips us with a method to verify summable or subexponential decay.

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