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A functional-analytical approach to the asymptotics of recursions

Author(s): Christian Pötzsche
Journal: Proc. Amer. Math. Soc. 137 (2009), 3297-3307.
MSC (2000): Primary 39A11; Secondary 46T20, 47H09, 47H10, 47J05, 65Q05
Posted: May 13, 2009
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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: 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
Posted: May 13, 2009
Communicated by: Andreas Seeger
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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