Construction of Floquet–Bloch Solutions and Estimation of Lengths of Resonance Zones of One-Dimensional Schrödinger Equation with Smooth Potential
A one-dimensional Schrödinger equation with a potential characterized by a certain rate of approximation by trigonometric polynomials is investigated by methods of the KAM theory. Estimates for resonance energy zones are obtained. The case where the potential belongs to the Gevrey class is analyzed....
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| Date: | 2004 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
2004
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3724 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860509856792838144 |
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| author | Denysenko, O. M. Parasyuk, I. O. Денисенко, О. М. Парасюк, І. О. |
| author_facet | Denysenko, O. M. Parasyuk, I. O. Денисенко, О. М. Парасюк, І. О. |
| author_sort | Denysenko, O. M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:05:58Z |
| description | A one-dimensional Schrödinger equation with a potential characterized by a certain rate of approximation by trigonometric polynomials is investigated by methods of the KAM theory. Estimates for resonance energy zones are obtained. The case where the potential belongs to the Gevrey class is analyzed. |
| first_indexed | 2026-03-24T02:47:45Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-3724 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:47:45Z |
| publishDate | 2004 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/fb/4fb47df0078176af1e8bd58a96614efb.pdf |
| spelling | umjimathkievua-article-37242020-03-18T20:05:58Z Construction of Floquet–Bloch Solutions and Estimation of Lengths of Resonance Zones of One-Dimensional Schrödinger Equation with Smooth Potential Побудова розв'язків Флоке - Блоха і оцінка довжин резонансних зон одповимірпого рівняння Шредінгера з гладким потенціалом Denysenko, O. M. Parasyuk, I. O. Денисенко, О. М. Парасюк, І. О. A one-dimensional Schrödinger equation with a potential characterized by a certain rate of approximation by trigonometric polynomials is investigated by methods of the KAM theory. Estimates for resonance energy zones are obtained. The case where the potential belongs to the Gevrey class is analyzed. Методами КАМ-теорії досліджено одновимірне рівняння Шредінгера з потенціалом, який характеризується певною швидкісно наближення тригонометричними поліномами. Одержано оцінки резонансних енергетичних зон. Проаналізовано випадок, коли потенціал належить класу Жевре. Institute of Mathematics, NAS of Ukraine 2004-01-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3724 Ukrains’kyi Matematychnyi Zhurnal; Vol. 56 No. 1 (2004); 3-18 Український математичний журнал; Том 56 № 1 (2004); 3-18 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/3724/4172 https://umj.imath.kiev.ua/index.php/umj/article/view/3724/4173 Copyright (c) 2004 Denysenko O. M.; Parasyuk I. O. |
| spellingShingle | Denysenko, O. M. Parasyuk, I. O. Денисенко, О. М. Парасюк, І. О. Construction of Floquet–Bloch Solutions and Estimation of Lengths of Resonance Zones of One-Dimensional Schrödinger Equation with Smooth Potential |
| title | Construction of Floquet–Bloch Solutions and Estimation of Lengths of Resonance Zones of One-Dimensional Schrödinger Equation with Smooth Potential |
| title_alt | Побудова розв'язків Флоке - Блоха і оцінка довжин
резонансних зон одповимірпого рівняння Шредінгера з гладким потенціалом |
| title_full | Construction of Floquet–Bloch Solutions and Estimation of Lengths of Resonance Zones of One-Dimensional Schrödinger Equation with Smooth Potential |
| title_fullStr | Construction of Floquet–Bloch Solutions and Estimation of Lengths of Resonance Zones of One-Dimensional Schrödinger Equation with Smooth Potential |
| title_full_unstemmed | Construction of Floquet–Bloch Solutions and Estimation of Lengths of Resonance Zones of One-Dimensional Schrödinger Equation with Smooth Potential |
| title_short | Construction of Floquet–Bloch Solutions and Estimation of Lengths of Resonance Zones of One-Dimensional Schrödinger Equation with Smooth Potential |
| title_sort | construction of floquet–bloch solutions and estimation of lengths of resonance zones of one-dimensional schrödinger equation with smooth potential |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3724 |
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