Upper bound for the diameter of a tree in the quantum graph theory
UDC 519.177We study two Sturm – Liouville spectral problems on an equilateral tree with continuity and Kirchhoff conditions at internal vertices and Neumann conditions at pendant vertices (first problem) and with Dirichlet conditions at pendant vertices (second problem). The spectrum of each of thes...
Збережено в:
| Дата: | 2022 |
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| Автори: | , , , , , , , |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2022
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/7176 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | UDC 519.177We study two Sturm – Liouville spectral problems on an equilateral tree with continuity and Kirchhoff conditions at internal vertices and Neumann conditions at pendant vertices (first problem) and with Dirichlet conditions at pendant vertices (second problem). The spectrum of each of these problems consists of infinitely many normal (isolated Fredholm) eigenvalues. It is shown that, knowing the asymptotics of the eigenvalues, it is possible to estimate the diameter of a tree from above for each of these problems. |
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| DOI: | 10.37863/umzh.v74i8.7176 |