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On the asymptotic summation of difference systems

Published online by Cambridge University Press:  23 July 2007

Harry Gingold  and
Fei Xue
Harry Gingold
Affiliation:
Department of Mathematics, West Virginia University, Morgantown, WV 26506-6310, USA ([email protected])
Fei Xue
Affiliation:
Department of Mathematics, Lynchburg College, 1501 Lakeside Drive, Lynchburg, VA 24501, USA ([email protected])
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Abstract

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 137 , Issue 4 , August 2007 , pp. 771 - 797
Copyright
2007 Royal Society of Edinburgh

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