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ON ONE CONDITION FOR THE DISCRETENESS OF THE SPECTRUM AND THE COMPACTNESS OF THE RESOLVENT OF A NONSECTORIAL STURM–LIOUVILLE OPERATOR ON THE SEMIAXIS
- Authors: Tumanov S.N.1
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Affiliations:
- Moscow Center of Fundamental and Applied Mathematics, Lomonosov Moscow State University
- Issue: Vol 510, No 1 (2023)
- Pages: 39-42
- Section: MATHEMATICS
- URL: https://ogarev-online.ru/2686-9543/article/view/134359
- DOI: https://doi.org/10.31857/S2686954323700145
- EDN: https://elibrary.ru/XJAIKI
- ID: 134359
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Abstract
The spectral properties of the Sturm–Liouville operator on the semi-axis with the complex-valued potential with the range exceeding the half-plane, has been little studied. The operator in this case can be non-sectorial, the numerical range can coincide with the entire complex plane. In this situation we propose the conditions ensuring the discreteness of the spectrum and the compactness of the resolvent.
About the authors
S. N. Tumanov
Moscow Center of Fundamental and Applied Mathematics, Lomonosov Moscow State University
Author for correspondence.
Email: sntumanov@yandex.ru
Russian Federation, Moscow
References
- Наймарк M.A. // Тр. ММО 1954. Т. 3. С. 181–270.
- Лидский В.Б. // Тр. ММО 1960. Т. 9. С. 45–79.
- Титчмарш Э.Ч. Разложения по собственным функциям, связанные с дифференциальными уравнениями второго порядка. Oxford, 1946. “Издательство иностранной литературы”, Москва, 1960.
- Sears D.B. // Canadian journ. math. 1950. V. 2. № 3. P. 314–325.
- Олвер Ф. Асимптотика и специальные функции. Academic Press, 1974. “Наука”, Физматлит, 1990.
- Наймарк M.A. ДАН 1952. Т. 85. С. 41–44.
- Ишкин Х.К. // Мат. заметки 2023. Т. 113.
- Tumanov S.N. // JDE 2022. V. 319. P. 80–99.
- Левин Б.Я. Распределение корней целых функций. Гос. Изд. Техн.-Теор. Лит., Москва, 1956.
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