Asymptotic approximations for second-order linear difference equations in Banach algebras, I

An asymptotic approximation theory is developed for some classes of linear second-order difference equations in Banach algebras, subject to “finite moments perturbations.” The special case of linear matrix difference equations (or, equivalently, of second-order systems) is included. Rigorous and exp...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 337; no. 2; pp. 1158 - 1170
Main Authors Soldà, Tania, Spigler, Renato, Vianello, Marco
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 15.01.2008
Elsevier
Subjects
Algebra
Banach algebras
Difference and functional equations, recurrence relations
Exact sciences and technology
Finite differences and functional equations
Finite moments asymptotics
Functional analysis
Linear and multilinear algebra, matrix theory
Mathematical analysis
Mathematics
Matrix difference equations
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Finite moments asymptotics
Matrix difference equations
Banach algebras
Second order equation
Second order
Error estimation
Perturbation
Difference equation
Banach algebra
Linear equation
Mathematical analysis
Approximation order
Approximation theory
Asymptotic approximation
Application
Matrix equation
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Summary:An asymptotic approximation theory is developed for some classes of linear second-order difference equations in Banach algebras, subject to “finite moments perturbations.” The special case of linear matrix difference equations (or, equivalently, of second-order systems) is included. Rigorous and explicitly computable bounds for the error terms are obtained.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2007.04.054