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| Content Provider | Springer Nature Link |
|---|---|
| Author | Berg, Lothar Krüppel, Manfred |
| Copyright Year | 2003 |
| Abstract | This paper deals with two-scale difference equations having a formal power series as symbol. We require that the equation has non-zero distributional solutions which are either compactly supported or integrals of compactly supported distributions with support bounded to the left. Such solutions are called eigenfunctions. As main result we determine the necessary and sufficient condition for the existence of eigenfunctions that the symbol must be a rational function with a special structure. We show that the eigenfunctions can be expressed by means of a finite sum of shifted eigenfunctions belonging to the case with a polynomial symbol (characteristic polynomial), which is well investigated. |
| Ending Page | 241 |
| Page Count | 16 |
| Starting Page | 226 |
| File Format | |
| ISSN | 03786218 |
| e-ISSN | 14209012 |
| Journal | Results in Mathematics |
| Issue Number | 3 |
| Volume Number | 44 |
| Language | English |
| Publisher | Birkhäuser-Verlag |
| Publisher Date | 2013-04-24 |
| Publisher Place | Basel |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Appell, Horn and Lauricella functions distributional solutions sums of shifted eigenfunctions rational symbols Operations with distributions Rational functions Equations for complex functions Mathematics Laplace transform |
| Content Type | Text |
| Resource Type | Article |
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