A functional-analytical approach to the asymptotics of recursions

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 qua...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2009-10, Vol.137 (10), p.3297-3307
Main Authors: PÖTZSCHE, Christian, SEEGER, Andreas
Format: Article
Language:English
Subjects:
Banach space
Cauchy problem
Difference and functional equations, recurrence relations
Difference equations
Exact sciences and technology
Finite differences and functional equations
Fixed point property
General mathematics
General, history and biography
Logical givens
Mathematical analysis
Mathematical inequalities
Mathematical sequences
Mathematical theorems
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Recursion
Sciences and techniques of general use
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Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-09-09360-5