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

 

A functional-analytical approach to the asymptotics of recursions


Author: Christian Pötzsche
Journal: Proc. Amer. Math. Soc. 137 (2009), 3297-3307
MSC (2000): Primary 39A11; Secondary 46T20, 47H09, 47H10, 47J05, 65Q05
Published electronically: May 13, 2009
MathSciNet review: 2515399
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Christian Pötzsche
Affiliation: Technische Universität München, Zentrum Mathematik, Boltzmannstraße 3, D-85748 Garching, Germany
Email: christian.poetzsche@ma.tum.de

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09360-5
PII: S 0002-9939(09)09360-5
Keywords: Recursion, iteration, nonautonomous difference equation, attractivity, $\ell ^p$-stability, admissibility, sequence space, functional-analytical method, measure of noncompactness
Received by editor(s): June 20, 2007
Received by editor(s) in revised form: August 27, 2007
Published electronically: May 13, 2009
Communicated by: Andreas Seeger
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.