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 q-difference equations case.
Recommended Citation
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
Department(s)
Mathematics and Statistics
Sponsor(s)
University of Missouri Research Board
Keywords and Phrases
Convolution; Time Scales; Q-Difference; Transport Equation
International Standard Serial Number (ISSN)
1085-3375
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2007 Hindawi, All rights reserved.
Publication Date
01 Jan 2007
