The Convolution on Time Scales
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2007-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2007/58373 |
| Summary: | 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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| ISSN: | 1085-3375 1687-0409 |