{"id":{"repo_id":"wfu","oai_identifier":"oai:wakespace.lib.wfu.edu:10339/14679"},"canonical_url":"https://search.dev.ndltd.org/etd/wfu/oai:wakespace.lib.wfu.edu:10339/14679","repository":{"repo_id":"wfu","name":"Wake Forest University","base_url":"https://wakespace.lib.wfu.edu/oai/request"},"display":{"title":"Some New Results on Difference Equations of Convolution Type","abstract":"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.","abstract_html":"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. 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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."]},{"key":"dc:title","label":"Title","values":["Some New Results on Difference Equations of Convolution Type"]}]}],"canonical_facts":{"dc:creator":["Vish, Nathaniel"],"dc:date.accessioned":["2009-05-06T15:18:57Z"],"dc:date.available":["2009-05-06T15:18:57Z"],"dc:date.issued":["2009-05-06T15:18:57Z"],"dc:description.abstract":["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."],"dc:identifier.uri":["http://hdl.handle.net/10339/14679"],"dc:language.iso":["en_US"],"dc:publisher":["Wake Forest University"],"dc:subject":["Difference Equations"],"dc:title":["Some New Results on Difference Equations of Convolution Type"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T22:00:55Z"}