The Convolution on Time Scales
Open Access
- 1 January 2007
- journal article
- research article
- Published by Hindawi Limited in Abstract and Applied Analysis
- Vol. 2007, 1-24
- https://doi.org/10.1155/2007/58373
Abstract
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-difference equations case.
Keywords
Funding Information
- University of Missouri
This publication has 3 references indexed in Scilit:
- Asymptotic expansions and analytic dynamic equationsZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2005
- Laplace transform and Z-transform: unification and extensionMethods and Applications of Analysis, 2002
- Basic Calculus on Time Scales and some of its ApplicationsResults in Mathematics, 1999