On completeness of the root function system of the $(2\times 2)$-Dirac operatorswith non-regular boundary conditions
- Authors: Makin A.S.1
-
Affiliations:
- Institute of Applied Mathematics and Mechanics, Donetsk
- Issue: Vol 89, No 3 (2025)
- Pages: 179-192
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/303961
- DOI: https://doi.org/10.4213/im9589
- ID: 303961
Cite item
Open Access
Access granted
Subscription Access
Abstract
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.
About the authors
Alexander Sergeevich Makin
Institute of Applied Mathematics and Mechanics, Donetsk
Author for correspondence.
Email: alexmakin@yandex.ru
Doctor of physico-mathematical sciences, Professor
References
- 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
Supplementary files
