On completeness of the root function system of the $(2\times 2)$-Dirac operatorswith non-regular boundary conditions
- 作者: Makin A.S.1
-
隶属关系:
- Institute of Applied Mathematics and Mechanics, Donetsk
- 期: 卷 89, 编号 3 (2025)
- 页面: 179-192
- 栏目: Articles
- URL: https://bakhtiniada.ru/1607-0046/article/view/303961
- DOI: https://doi.org/10.4213/im9589
- ID: 303961
如何引用文章
详细
The paper is concerned with completeness of the system of root functions of the$(2\times2)$-Dirac operator with summable complex-valued potential and non-regular boundary conditions. Sufficient conditions for completeness of the root function system of this operator are found.
作者简介
Alexander Makin
Institute of Applied Mathematics and Mechanics, Donetsk
编辑信件的主要联系方式.
Email: alexmakin@yandex.ru
Doctor of physico-mathematical sciences, Professor
参考
- G. D. Birkhoff, R. E. Langer, “The boundary problems and developments associated with a system of ordinary linear differential equations of the first order”, Proc. Amer. Acad. Arts Sci., 58:2 (1923), 49–128
- Ю. П. Гинзбург, “О почти инвариантных спектральных свойствах сжатий и мультипликативных свойствах аналитических оператор-функций”, Функц. анализ и его прил., 5:3 (1971), 32–41
- В. А. Марченко, Операторы Штурма–Лиувилля и их приложения, Наукова Думка, Киев, 1977, 331 с.
- M. M. Malamud, L. L. Oridoroga, “On the completeness of root subspaces of boundary value problems for first order systems of ordinary differential equations”, J. Funct. Anal., 263:7 (2012), 1939–1980
- М. М. Маламуд, Л. Л. Оридорога, “Теоремы полноты для систем дифференциальных уравнений”, Функц. анализ и его прил., 34:4 (2000), 88–90
- A. V. Agibalova, M. M. Malamud, L. L. Oridoroga, “On the completeness of general boundary value problems for $2times2$ first order systems of ordinary differential equations”, Methods Funct. Anal. Topol., 18:1 (2012), 4–18
- A. A. Lunyov, M. M. Malamud, “On spectral synthesis for dissipative Dirac type operators”, Integral Equations Operator Theory, 80:1 (2014), 79–106
- A. A. Lunyov, M. M. Malamud, “On the completeness and Riesz basis property of root subspaces of boundary value problems for first order systems and applications”, J. Spectr. Theory, 5:1 (2015), 17–70
- A. A. Лунeв, M. M. Maламуд, “О полноте системы корневых векторов для систем первого порядка. Применение к задаче Редже”, Докл. РАН, 453:3 (2013), 256–261
- А. П. Косарев, А. А. Шкаликов, “Спектральные асимптотики решений $2times 2$-системы обыкновенных дифференциальных уравнений первого порядка”, Матем. заметки, 110:6 (2021), 939–943
- A. Makin, “On the completeness of root function system of the Dirac operator with two-point boundary conditions”, Math. Nachr., 297:7 (2024), 2468–2487
- A. A. Lunyov, M. M. Malamud, “On the completeness property of root vector systems for $2times2$ Dirac type operators with non-regular boundary conditions”, J. Math. Anal. Appl., 543:2, Part 1 (2025), 128949, 42 pp.
- A. M. Savchuk, A. A. Shkalikov, “The Dirac operator with complex-valued summable potential”, Math. Notes, 96:5 (2014), 777–810
- A. A. Lunyov, M. M. Malamud, “On the Riesz basis property of root vectors system for $2times2$ Dirac type operators”, J. Math. Anal. Appl., 441:1 (2016), 57–103
- A. A. Лунeв, M. M. Maламуд, “О базисности Рисса системы корневых векторов для $(2times2)$-системы типа Дирака”, Докл. РАН, 458:3 (2014), 255–260
- A. Makin, “On convergence of spectral expansions of Dirac operators with regular boundary conditions”, Math. Nachr., 295:1 (2022), 189–210
- A. A. Lunyov, M. M. Malamud, On transformation operators and Riesz basis property of root vectors system for $ntimes n$ Dirac type operators. Application to the Timoshenko beam model
补充文件
