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...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2007-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2007/58373 |
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doaj-cb30023e3b8e4bffbbad56816536fd0b2020-11-24T22:26:28ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092007-01-01200710.1155/2007/5837358373The Convolution on Time ScalesMartin Bohner0Gusein Sh. Guseinov1Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla, MO 65401, USADepartment of Mathematics, Atilim University, Incek, Ankara 06836, TurkeyThe 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.http://dx.doi.org/10.1155/2007/58373 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Martin Bohner Gusein Sh. Guseinov |
| spellingShingle |
Martin Bohner Gusein Sh. Guseinov The Convolution on Time Scales Abstract and Applied Analysis |
| author_facet |
Martin Bohner Gusein Sh. Guseinov |
| author_sort |
Martin Bohner |
| title |
The Convolution on Time Scales |
| title_short |
The Convolution on Time Scales |
| title_full |
The Convolution on Time Scales |
| title_fullStr |
The Convolution on Time Scales |
| title_full_unstemmed |
The Convolution on Time Scales |
| title_sort |
convolution on time scales |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2007-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/2007/58373 |
| work_keys_str_mv |
AT martinbohner theconvolutionontimescales AT guseinshguseinov theconvolutionontimescales AT martinbohner convolutionontimescales AT guseinshguseinov convolutionontimescales |
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1725753458135400448 |