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

• Published in: Journal of mathematical analysis and applications Vol. 337; no. 2; pp. 1158 - 1170
• Main Authors: Soldà, Tania, Spigler, Renato, Vianello, Marco
• Format: Journal Article
• Language: English
• 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

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...