Eigenvalues of Sturm-Liouville operators and prime numbers
We show that there is no function $q(x)\in L_2(0,1)$ which is the potential of a Sturm-Liouville problem with Dirichlet boundary condition whose spectrum is a set depending nonlinearly on the set of prime numbers as suggested by Mingarelli [7].
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2017-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2017/50/abstr.html |
| _version_ | 1818274831073804288 |
|---|---|
| author | Rauf Amirov Ibrahim Adalar |
| author_facet | Rauf Amirov Ibrahim Adalar |
| author_sort | Rauf Amirov |
| collection | DOAJ |
| description | We show that there is no function $q(x)\in L_2(0,1)$ which is the potential
of a Sturm-Liouville problem with Dirichlet boundary condition whose spectrum
is a set depending nonlinearly on the set of prime numbers as suggested by
Mingarelli [7]. |
| first_indexed | 2024-12-12T22:20:06Z |
| format | Article |
| id | doaj.art-bbcaf2523dea48f59a0907911fd0da21 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-12T22:20:06Z |
| publishDate | 2017-02-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-bbcaf2523dea48f59a0907911fd0da212022-12-22T00:09:56ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912017-02-01201750,13Eigenvalues of Sturm-Liouville operators and prime numbersRauf Amirov0Ibrahim Adalar1 Cumhuriyet Univ., 58140 Sivas, Turkey Cumhuriyet Univ., Zara/Sivas, Turkey We show that there is no function $q(x)\in L_2(0,1)$ which is the potential of a Sturm-Liouville problem with Dirichlet boundary condition whose spectrum is a set depending nonlinearly on the set of prime numbers as suggested by Mingarelli [7].http://ejde.math.txstate.edu/Volumes/2017/50/abstr.htmlSturm-Liouvillespectrumprime numbers |
| spellingShingle | Rauf Amirov Ibrahim Adalar Eigenvalues of Sturm-Liouville operators and prime numbers Electronic Journal of Differential Equations Sturm-Liouville spectrum prime numbers |
| title | Eigenvalues of Sturm-Liouville operators and prime numbers |
| title_full | Eigenvalues of Sturm-Liouville operators and prime numbers |
| title_fullStr | Eigenvalues of Sturm-Liouville operators and prime numbers |
| title_full_unstemmed | Eigenvalues of Sturm-Liouville operators and prime numbers |
| title_short | Eigenvalues of Sturm-Liouville operators and prime numbers |
| title_sort | eigenvalues of sturm liouville operators and prime numbers |
| topic | Sturm-Liouville spectrum prime numbers |
| url | http://ejde.math.txstate.edu/Volumes/2017/50/abstr.html |
| work_keys_str_mv | AT raufamirov eigenvaluesofsturmliouvilleoperatorsandprimenumbers AT ibrahimadalar eigenvaluesofsturmliouvilleoperatorsandprimenumbers |