On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials
We provide the proof of a practical pointwise characterization of the set RP defined by the closure set of the real projections of the zeros of an exponential polynomial P(z)=∑j=1ncjewjz with real frequencies wj linearly independent over the rationals. As a consequence, we give a complete descriptio...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/3605690 |
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| _version_ | 1850179451186315264 |
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| author | J. M. Sepulcre |
| author_facet | J. M. Sepulcre |
| author_sort | J. M. Sepulcre |
| collection | DOAJ |
| description | We provide the proof of a practical pointwise characterization of the set RP defined by the closure set of the real projections of the zeros of an exponential polynomial P(z)=∑j=1ncjewjz with real frequencies wj linearly independent over the rationals. As a consequence, we give a complete description of the set RP and prove its invariance with respect to the moduli of the cj′s, which allows us to determine exactly the gaps of RP and the extremes of the critical interval of P(z) by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance. |
| format | Article |
| id | doaj-art-9c66908f486049a2ab536fc727baf37e |
| institution | OA Journals |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-9c66908f486049a2ab536fc727baf37e2025-08-20T02:18:29ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/36056903605690On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential PolynomialsJ. M. Sepulcre0Department of Mathematics, University of Alicante, 03080 Alicante, SpainWe provide the proof of a practical pointwise characterization of the set RP defined by the closure set of the real projections of the zeros of an exponential polynomial P(z)=∑j=1ncjewjz with real frequencies wj linearly independent over the rationals. As a consequence, we give a complete description of the set RP and prove its invariance with respect to the moduli of the cj′s, which allows us to determine exactly the gaps of RP and the extremes of the critical interval of P(z) by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance.http://dx.doi.org/10.1155/2016/3605690 |
| spellingShingle | J. M. Sepulcre On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials Journal of Function Spaces |
| title | On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials |
| title_full | On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials |
| title_fullStr | On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials |
| title_full_unstemmed | On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials |
| title_short | On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials |
| title_sort | on the result of invariance of the closure set of the real projections of the zeros of an important class of exponential polynomials |
| url | http://dx.doi.org/10.1155/2016/3605690 |
| work_keys_str_mv | AT jmsepulcre ontheresultofinvarianceoftheclosuresetoftherealprojectionsofthezerosofanimportantclassofexponentialpolynomials |