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.
G. S. Guseinov and M. Bohner, "The Convolution on Time Scales," Abstract and Applied Analysis, Hindawi, Jan 2007.
The definitive version is available at https://doi.org/10.1155/2007/58373
Mathematics and Statistics
University of Missouri Research Board
Keywords and Phrases
Convolution; Time Scales; Q-Difference; Transport Equation
Article - Journal
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