Eigenvalues asymptotics for Stark operators
We give the eigenvalues asymptotics for the Stark operator of the form $\displaystyle-\Delta+Fx$, $F>0$ on $\displaystyle\mathrm{L}^2([0,d])$. This is given in the case when $F$ is small enough or sufficiently large. We impose various boundary conditions. The proof is based on the asymptotics o...
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| Format: | Article |
| Language: | English |
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EJAAM
2019-07-01
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| Series: | E-Journal of Analysis and Applied Mathematics |
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| Online Access: | https://ejaam.org/articles/2019/10.2478-ejaam-2019-0001.pdf |
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| _version_ | 1823864950186049536 |
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| author | Hatem Najar Monia Raissi |
| author_facet | Hatem Najar Monia Raissi |
| author_sort | Hatem Najar |
| collection | DOAJ |
| description | We give the eigenvalues asymptotics for the Stark operator of the form $\displaystyle-\Delta+Fx$, $F>0$ on $\displaystyle\mathrm{L}^2([0,d])$. This is given in the case when $F$ is small enough or sufficiently large. We impose various boundary conditions. The proof is based on the asymptotics of the specialized Airy functions. |
| format | Article |
| id | doaj-art-ef0db9362f1643b58c42e002cf24d79c |
| institution | Kabale University |
| issn | 2544-9990 |
| language | English |
| publishDate | 2019-07-01 |
| publisher | EJAAM |
| record_format | Article |
| series | E-Journal of Analysis and Applied Mathematics |
| spelling | doaj-art-ef0db9362f1643b58c42e002cf24d79c2025-02-08T18:35:22ZengEJAAME-Journal of Analysis and Applied Mathematics2544-99902019-07-01201910.2478/ejaam-2019-0001Eigenvalues asymptotics for Stark operatorsHatem Najar0Monia Raissi1Département de Mathématiques, Faculté des Sciences de Moanstir, 5019 Monastir, TunisiaDépartement de Mathématiques, Faculté des Sciences de Moanstir, 5019 Monastir, TunisiaWe give the eigenvalues asymptotics for the Stark operator of the form $\displaystyle-\Delta+Fx$, $F>0$ on $\displaystyle\mathrm{L}^2([0,d])$. This is given in the case when $F$ is small enough or sufficiently large. We impose various boundary conditions. The proof is based on the asymptotics of the specialized Airy functions.https://ejaam.org/articles/2019/10.2478-ejaam-2019-0001.pdfspectral theoryschrödinger operatordirichlet and neumann laplacianstark operatoreigenvalue problemairy functions |
| spellingShingle | Hatem Najar Monia Raissi Eigenvalues asymptotics for Stark operators E-Journal of Analysis and Applied Mathematics spectral theory schrödinger operator dirichlet and neumann laplacian stark operator eigenvalue problem airy functions |
| title | Eigenvalues asymptotics for Stark operators |
| title_full | Eigenvalues asymptotics for Stark operators |
| title_fullStr | Eigenvalues asymptotics for Stark operators |
| title_full_unstemmed | Eigenvalues asymptotics for Stark operators |
| title_short | Eigenvalues asymptotics for Stark operators |
| title_sort | eigenvalues asymptotics for stark operators |
| topic | spectral theory schrödinger operator dirichlet and neumann laplacian stark operator eigenvalue problem airy functions |
| url | https://ejaam.org/articles/2019/10.2478-ejaam-2019-0001.pdf |
| work_keys_str_mv | AT hatemnajar eigenvaluesasymptoticsforstarkoperators AT moniaraissi eigenvaluesasymptoticsforstarkoperators |