q-Dominant and q-recessive matrix solutions for linear quantum systems
In this study, linear second-order matrix $q$-difference equations are shown to be formally self-adjoint equations with respect to a certain inner product and the associated self-adjoint boundary conditions. A generalized Wronskian is introduced and a Lagrange identity and Abel's formula are es...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2007-05-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=270 |
| _version_ | 1797830781880500224 |
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| author | Douglas Anderson L. M. Moats |
| author_facet | Douglas Anderson L. M. Moats |
| author_sort | Douglas Anderson |
| collection | DOAJ |
| description | In this study, linear second-order matrix $q$-difference equations are shown to be formally self-adjoint equations with respect to a certain inner product and the associated self-adjoint boundary conditions. A generalized Wronskian is introduced and a Lagrange identity and Abel's formula are established. Two reduction-of-order theorems are given. The analysis and characterization of $q$-dominant and $q$-recessive solutions at infinity are presented, emphasizing the case when the quantum system is disconjugate. |
| first_indexed | 2024-04-09T13:41:37Z |
| format | Article |
| id | doaj.art-6c36c7a5edad4da0a17e7dc333773928 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:41:37Z |
| publishDate | 2007-05-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-6c36c7a5edad4da0a17e7dc3337739282023-05-09T07:52:58ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752007-05-0120071112910.14232/ejqtde.2007.1.11270q-Dominant and q-recessive matrix solutions for linear quantum systemsDouglas Anderson0L. M. Moats1Concordia College, Moorhead, MN, U.S.A.Concordia College, Moorhead, MN, U.S.A.In this study, linear second-order matrix $q$-difference equations are shown to be formally self-adjoint equations with respect to a certain inner product and the associated self-adjoint boundary conditions. A generalized Wronskian is introduced and a Lagrange identity and Abel's formula are established. Two reduction-of-order theorems are given. The analysis and characterization of $q$-dominant and $q$-recessive solutions at infinity are presented, emphasizing the case when the quantum system is disconjugate.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=270 |
| spellingShingle | Douglas Anderson L. M. Moats q-Dominant and q-recessive matrix solutions for linear quantum systems Electronic Journal of Qualitative Theory of Differential Equations |
| title | q-Dominant and q-recessive matrix solutions for linear quantum systems |
| title_full | q-Dominant and q-recessive matrix solutions for linear quantum systems |
| title_fullStr | q-Dominant and q-recessive matrix solutions for linear quantum systems |
| title_full_unstemmed | q-Dominant and q-recessive matrix solutions for linear quantum systems |
| title_short | q-Dominant and q-recessive matrix solutions for linear quantum systems |
| title_sort | q dominant and q recessive matrix solutions for linear quantum systems |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=270 |
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