Spectral Analysis of Higher-Order Differential Operators with Discontinuity Conditions at an Interior Point
- Authors: Yurko VA1
-
Affiliations:
- Chernyshevskii Saratov National Research State University
- Issue: Vol 63, No 2 (2017): Proceedings of the Crimean Autumn Mathematical School-Symposium
- Pages: 362-372
- Section: New Results
- URL: https://journals.rudn.ru/CMFD/article/view/22388
- DOI: https://doi.org/10.22363/2413-3639-2017-63-2-362-372
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Abstract
Higher-order differential operators on a finite interval with jump conditions inside the interval are studied. Properties of spectral characteristics are obtained, and completeness and expansion theorems are proved for this class of operators.
About the authors
V A Yurko
Chernyshevskii Saratov National Research State University
Email: yurkova@info.sgu.ru
83 Astrahanskaya st., 410026 Saratov, Russia
References
- Левитан Б. М., Саргсян И. С. Введение в спектральную теорию. - М.: Наука, 1970.
- Литвиненко О. Н., Сошников В. И. Теория неоднородных линий и их применение в радиотехнике. - М.: Сов. радио, 1964.
- Мещанов В. П., Фельдштейн А. Л. Автоматизированное проектирование направленных ответвителей СВЧ. - М.: Связь, 1980.
- Наймарк М. А. Линейные дифференциальные операторы. - М.: Наука, 1969.
- Юрко В. А. О краевых задачах с условиями разрыва внутри интервала// Дифф. уравн. - 2000. - 36, № 8. - С. 1139-1140.
- Amirov R., Ozkan A. Discontinuous Sturm-Liouville problems with eigenvalue dependent boundary conditions// Math. Phys. Anal. Geom. - 2014. - 17, № 3-4. - С. 483-491.
- Anderssen R. S. The effect of discontinuities in density and shear velocity on the asymptotic overtone structure of torsional eigenfrequencies of the Earth// Geophys. J. R. Astr. Soc. - 1997. - 50. - С. 303- 309.
- Beals R., Deift P., Tomei C. Direct and inverse scattering on the line. - Providence: Am. Math. Soc., 1988.
- Freiling G., Yurko V. A. Inverse Sturm-Liouville problems and their applications. - New York: NOVA Science Publishers, 2001.
- Hald O. H. Discontinuous inverse eigenvalue problems// Commun. Pure Appl. Math. - 1984. - 37.- С. 539-577.
- Krueger R. J. Inverse problems for nonabsorbing media with discontinuous material properties// J. Math. Phys. - 1982. - 23, № 3. - С. 396-404.
- Lapwood F. R., Usami T. Free oscillations of the Earth. - Cambridge: Cambridge University Press, 1981.
- Shepelsky D. G. The inverse problem of reconstruction of the medium‘s conductivity in a class of discontinuous and increasing functions// Adv. Sov. Math. - 1994. - 19. - С. 209-231.
- Yurko V. A. Integral transforms connected with discontinuous boundary value problems// Integral Transforms Spec. Funct. - 2000. - 10, № 2. - С. 141-164.
- Yurko V. A. Method of spectral mappings in the inverse problem theory. - Utrecht: VSP, 2002.
