Some New Results on Difference Equations of Convolution Type

In this thesis we consider convolution type linear difference equations with coefficients satisfying some monotonicity properties. Methods from renewal theory are employed to obtain easily verified conditions for asymptotic stability of the zero solution, in terms of the coefficient sequence. Explicit bounds and rates of convergence are considered. We use these results to provide some new bounds for inverses of positive triangular matrices with monotonic column entries. We also refine a result of Vecchio and Mallik. This new result is shown to be in a sense best possible under the given constraints.

Grantor dc:publisher

Wake Forest University

Year dc:date.issued

2009

Author dc:creator

• Vish, Nathaniel

• Difference Equations

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/10339/14679

OAI identifier oai:identifier

oai:wakespace.lib.wfu.edu:10339/14679