The asymptotic solution of linear differential systems

On asymptotic summation of potentially oscillatory difference systems

A new method for asymptotic summation of linear systems of difference equations is proposed and studied. It is based on the introduction of a certain summation equation that pinpoints sufficient conditions for asymptotic summation. These conditions serve as a framework from which new and old theorems follow. In particular the analogues of the fundamental theorems of Levinson and Hartman and Wintner are shown to follow from one and the same framework. Examples are given that are not amenable to other techniques.

On the asymptotic summation of difference systems

Linear homogeneous difference systems of equations on an infinite interval are considered. Conditions are given which allow to represent a fundamental solution as a product of two square matrices. The product is made of a diagonal matrix and a matrix which is a perturbation of the identity. The diagonal matrix being on the left in the proposed product rather than on the right as it has been traditionally represented. A self contained theorem of asymptotic approximation is provided which is applied to a special family of difference systems. A theorem, utilizing a linear transformation, which is best possible in a certain sense, is also given.

Almost diagonal systems of linear difference equations

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Almost diagonal systems of linear difference equations