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Asymptotic Representation of Solutions of Perturbed Systems of Linear Difference Equations
Author(s) -
Benzaid Z.,
Lutz D. A.
Publication year - 1987
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1987773195
Subject(s) - diagonal , mathematics , equivalence (formal languages) , perturbation (astronomy) , mathematical analysis , pure mathematics , representation (politics) , diagonal matrix , physics , geometry , quantum mechanics , politics , political science , law
Our purpose is to asymptotically represent solutions of linear difference equations x ( k + 1) = [ A 0 + A ( k )] x ( k ) when k → + ∞ and A ( k ) is “small” by transforming them into so‐called L ‐diagonal form. Two properties are then responsible for the asymptotic equivalence of an L ‐diagonal form to a diagonal one: a dichotomy condition on the diagonal part, and a growth condition on the perturbation term. In this manner, we derive some known asymptotic results from a central point of view and also several new extensions and generalizations of them. Some examples are constructed which demonstrate the need for a dichotomy‐type condition, which shows incidentally that results of M. A. Evgrafov are incorrect, since they omit such a condition.