The form of the spectral function associated with Sturm-Liouville problems for small values of the spectral parameter
We study the linear second-order differential equation $$ -y'' + q(x) y = lambda y $$ where, amongst other conditions, $q in L^1[0,infty)$. We obtain a convergent series expansion for the spectral function which is valid for small values of $lambda$. We also derive an asymptotic rep...
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| Format: | Article |
| Language: | English |
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Texas State University
2013-01-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/17/abstr.html |
| _version_ | 1818365833226747904 |
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| author | B. J. Harris |
| author_facet | B. J. Harris |
| author_sort | B. J. Harris |
| collection | DOAJ |
| description | We study the linear second-order differential equation $$ -y'' + q(x) y = lambda y $$ where, amongst other conditions, $q in L^1[0,infty)$. We obtain a convergent series expansion for the spectral function which is valid for small values of $lambda$. We also derive an asymptotic representation. |
| first_indexed | 2024-12-13T22:26:32Z |
| format | Article |
| id | doaj.art-85d270b6263f41e8b002dde2c848cd5a |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-13T22:26:32Z |
| publishDate | 2013-01-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-85d270b6263f41e8b002dde2c848cd5a2022-12-21T23:29:12ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912013-01-01201317,15The form of the spectral function associated with Sturm-Liouville problems for small values of the spectral parameterB. J. HarrisWe study the linear second-order differential equation $$ -y'' + q(x) y = lambda y $$ where, amongst other conditions, $q in L^1[0,infty)$. We obtain a convergent series expansion for the spectral function which is valid for small values of $lambda$. We also derive an asymptotic representation.http://ejde.math.txstate.edu/Volumes/2013/17/abstr.htmlSturm Liouville equationspectral functionsmall eigenparameter |
| spellingShingle | B. J. Harris The form of the spectral function associated with Sturm-Liouville problems for small values of the spectral parameter Electronic Journal of Differential Equations Sturm Liouville equation spectral function small eigenparameter |
| title | The form of the spectral function associated with Sturm-Liouville problems for small values of the spectral parameter |
| title_full | The form of the spectral function associated with Sturm-Liouville problems for small values of the spectral parameter |
| title_fullStr | The form of the spectral function associated with Sturm-Liouville problems for small values of the spectral parameter |
| title_full_unstemmed | The form of the spectral function associated with Sturm-Liouville problems for small values of the spectral parameter |
| title_short | The form of the spectral function associated with Sturm-Liouville problems for small values of the spectral parameter |
| title_sort | form of the spectral function associated with sturm liouville problems for small values of the spectral parameter |
| topic | Sturm Liouville equation spectral function small eigenparameter |
| url | http://ejde.math.txstate.edu/Volumes/2013/17/abstr.html |
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