On recovering the shape of a quantum tree from the spectrum of the Dirichlet boundary problem
Spectral problems are considered generated by the Sturm-Liouville equation on equilateral trees with the Dirichlet boundary conditions at the pendant vertices and continuity and Kirchhoff's conditions at the interior vertices. It is proved that there are no co-spectral (i.e., having the same sp...
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| Format: | Article |
| Language: | deu |
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Ivan Franko National University of Lviv
2023-12-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/412 |
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| author | O. Boyko O. Martynyuk V. Pivovarchik |
| author_facet | O. Boyko O. Martynyuk V. Pivovarchik |
| author_sort | O. Boyko |
| collection | DOAJ |
| description | Spectral problems are considered generated by the Sturm-Liouville equation on equilateral trees with the Dirichlet boundary conditions at the pendant vertices and continuity and Kirchhoff's conditions at the interior vertices. It is proved that there are no co-spectral (i.e., having the same spectrum of such problem) among equilateral trees of $\leq 8$ vertices. All co-spectral trees of $9$ vertices are presented. |
| format | Article |
| id | doaj-art-327de690b60343ffb034917fea99b1ff |
| institution | Kabale University |
| issn | 1027-4634 2411-0620 |
| language | deu |
| publishDate | 2023-12-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-327de690b60343ffb034917fea99b1ff2025-08-20T03:33:11ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342411-06202023-12-0160216217210.30970/ms.60.2.162-172412On recovering the shape of a quantum tree from the spectrum of the Dirichlet boundary problemO. Boyko0O. Martynyuk1V. Pivovarchik2South Ukrainian National Pedagogical University Odesa, UkraineSouth Ukrainian National Pedagogical University Odesa, UkraineSouth Ukrainian National Pedagogical University Odesa, UkraineSpectral problems are considered generated by the Sturm-Liouville equation on equilateral trees with the Dirichlet boundary conditions at the pendant vertices and continuity and Kirchhoff's conditions at the interior vertices. It is proved that there are no co-spectral (i.e., having the same spectrum of such problem) among equilateral trees of $\leq 8$ vertices. All co-spectral trees of $9$ vertices are presented.http://matstud.org.ua/ojs/index.php/matstud/article/view/412tree;adjacency matrix;eigenvalues;asymptotics;potential;dirichlet condition;neumann condition;sturm-liouville equation;characteristic function;normalized laplacian |
| spellingShingle | O. Boyko O. Martynyuk V. Pivovarchik On recovering the shape of a quantum tree from the spectrum of the Dirichlet boundary problem Математичні Студії tree; adjacency matrix; eigenvalues; asymptotics; potential; dirichlet condition; neumann condition; sturm-liouville equation; characteristic function; normalized laplacian |
| title | On recovering the shape of a quantum tree from the spectrum of the Dirichlet boundary problem |
| title_full | On recovering the shape of a quantum tree from the spectrum of the Dirichlet boundary problem |
| title_fullStr | On recovering the shape of a quantum tree from the spectrum of the Dirichlet boundary problem |
| title_full_unstemmed | On recovering the shape of a quantum tree from the spectrum of the Dirichlet boundary problem |
| title_short | On recovering the shape of a quantum tree from the spectrum of the Dirichlet boundary problem |
| title_sort | on recovering the shape of a quantum tree from the spectrum of the dirichlet boundary problem |
| topic | tree; adjacency matrix; eigenvalues; asymptotics; potential; dirichlet condition; neumann condition; sturm-liouville equation; characteristic function; normalized laplacian |
| url | http://matstud.org.ua/ojs/index.php/matstud/article/view/412 |
| work_keys_str_mv | AT oboyko onrecoveringtheshapeofaquantumtreefromthespectrumofthedirichletboundaryproblem AT omartynyuk onrecoveringtheshapeofaquantumtreefromthespectrumofthedirichletboundaryproblem AT vpivovarchik onrecoveringtheshapeofaquantumtreefromthespectrumofthedirichletboundaryproblem |