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2007 The Convolution on Time Scales
Martin Bohner, Gusein Sh. Guseinov
Abstr. Appl. Anal. 2007: 1-24 (2007). DOI: 10.1155/2007/58373


The main theme in this paper is an initial value problem containing a dynamic version of the transport equation. Via this problem, the delay (or shift) of a function defined on a time scale is introduced, and the delay in turn is used to introduce the convolution of two functions defined on the time scale. In this paper, we give some elementary properties of the delay and of the convolution and we also prove the convolution theorem. Our investigation contains a study of the initial value problem under consideration as well as some results about power series on time scales. As an extensive example, we consider the q -difference equations case.


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Martin Bohner. Gusein Sh. Guseinov. "The Convolution on Time Scales." Abstr. Appl. Anal. 2007 1 - 24, 2007.


Published: 2007
First available in Project Euclid: 27 February 2008

zbMATH: 1155.39010
MathSciNet: MR2320804
Digital Object Identifier: 10.1155/2007/58373

Rights: Copyright © 2007 Hindawi

Vol.2007 • 2007
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