A Generalization of Wiener's Lemma and its Application to Volterra Difference Equations on a Banach Space
Furumochi, Tetsuo; Murakami, Satoru; Nagabuchi, Yutaka; Furumochi, Tetsuo; Department of Mathematics, Shimane University; Murakami, Satoru; Department of Applied Mathematics, Okayama University of Science; Nagabuchi, Yutaka; Department of Systems and Control Engineering, Anan National College of Technology
Журнал:
Journal of Difference Equations and Applications
Дата:
2004
Аннотация:
Some stability properties for the zero solution of linear Volterra difference equations on a Banach space are studied in connection with the summability of the fundamental solution and the invertibility of the characteristic operator. A key is to extend Wiener's lemma for absolutely convergent scalar sequences to summable sequences of bounded linear operators on a Banach space by applying certain result in commutative Banach algebras.
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