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JOURNALS // Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva

Zhurnal SVMO, 2020, Volume 22, Number 3, Pages 280–305 (Mi svmo773)

On the asymptotic behavior of the spectrum of a sixth-order differential operator, whose potential is the delta function
S. I. Mitrokhin

References

1. F. A. Berezin, L. D. Faddeev, “Remarks on the Schrodinger equation with a singular potential”, Doklady Akademii nauk SSSR, 137:5 (1961), 1011–1014 (In Russ.)  mathnet  mathscinet  zmath
2. O. Z. Peng, X. Wang, J. Y. Zeng, “Analytic solution to the Schrodinger equation with a harmonic oscillator potential plus $\delta$-potential”, Sci. China, Ser. A., 34:10 (1991), 1215–1221  mathscinet  zmath
3. S. Fassari, G. Inglese, “On the spectrum of the harmonic oscillator with a $\delta$-type pertubation”, Helv. Phys. Acta., 67:6 (1994), 650–659  mathscinet  zmath
4. S. Fassari, G. Inglese, “On the spectrum of the harmonic oscillator with a $\delta$-type pertubation”, Annales Henri Poincare, 70:6 (1997), 858–865  mathscinet  zmath
5. V. D. Krevchik, R. V. Zaitsev, “Impurity absorption of light in structures with quantum dots”, Physics of the Solid State, 43:3 (2001), 504–507 (In Russ.)  crossref
6. V. A. Il’in, “Convergence of eigenfunction expansions at points of discontinuity of the coefficients of a differential operator”, Mathematical Notes of the Academy of Sciences of the USSR, 22:5 (1977), 670–872  mathnet
7. S. I. Mitrokhin, “Regularized trace formulas for second-order differential operators with discontinuous coefficients”, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 22:6 (1986), 3–6 (In Russ.)  mathnet  mathscinet
8. S. I. Mitrokhin, “On trace formulas for a boundary value problem with a functional differential equation with a discontinuous coefficient”, Differential Equations, 22:6 (1986), 927–931 (In Russ.)  mathnet  mathscinet  zmath
9. V. A. Il’in, “Necessary and sufficient conditions for being a Riesz basis of root vectors of second-order discontinuous operators”, Differential Equations, 22:12 (1986), 2059–2071 (In Russ.)  mathnet  mathscinet  mathscinet  zmath
10. S. I. Mitrokhin, “On some spectral properties of second-order differential operators with discontinuous weight function”, Doklady Akademii nauk, 356:1 (1997), 13–15 (In Russ.)  mathnet  mathscinet  zmath
11. V. A. Vinokurov, V. A. Sadovnichy, “Asymptotics of any order for the eigenvalues and eigenfunctions of the Sturm-Liouville boundary-value problem on a segment with a summable potential”, Izvestiya: Mathematics, 64:4 (2000), 695–754  mathnet  mathscinet  zmath
12. S. I. Mitrokhin, “Spectral properties of a fourth-order differential operator with integrable coefficients”, Proceedings of the Steklov Institute of Mathematics, 270 (2010), 184–193  mathnet  mathscinet  zmath
13. S. I. Mitrokhin, “Spectral properties of boundary value problems for a functional differential equation with summable coefficients”, Differential Equations, 46:8 (2010), 1085–1093 (In Russ.)  crossref  mathscinet  zmath
14. S. I. Mitrokhin, “Spectral properties of even-order differential operators with summable coefficients”, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 17:4, 3–15 (In Russ.)  mathnet  mathscinet
15. S. I. Mitrokhin, “Asymptotics of the spectrum of a periodic boundary value problem for a differential operator with a summable potential”, Trudy instituta matematiki i mekhaniki URO RAN, 25:1 (2019), 136–149 (In Russ.)  mathnet  crossref  mathscinet
16. A. M. Savchuk, A. A. Shkalikov, “Sturm-Liouville operators with singular potentials”, Mathematical Notes, 66:6 (1999), 741–753  mathnet  zmath
17. A. M. Savchuk, “First-order regularised trace of the Sturm-Liouville operator with $\delta$-potential”, Russian Mathematical Surveys, 55:6 (2000), 1168–1169  mathnet  mathscinet  zmath
18. V. A. Vinokurov, V. A. Sadovnichy, “The asymptotics of eigenvalues and eigenfunctions and a trace formula for a potential with delta functions”, Differential Equations, 38:6 (2002), 772–789  mathnet  mathscinet  zmath
19. A. M. Savchuk, A. A. Shkalikov, “Trace formula for Sturm-Liouville Operators with singular potentials”, Mathematical Notes, 69:3 (2001), 387–400  mathnet  mathscinet  zmath
20. V. A. Geiler, V. A. Margulis, I. I. Chuchaev, “Potentials of zero radius and Carleman operators”, Siberian Mathematical Journal, 36:4 (1995), 714–726  mathnet  crossref  mathscinet
21. D. I. Borisov, “Gaps in the spectrum of the Laplacian in a strip with periodic delta interaction”, Proceedings of the Steklov Institute of Mathematics (Supplementary Issues), 305:suppl. 1 (2019), S16–S23  mathnet
22. M. A. Naimark, Linear differential operators, Nauka Publ., Moscow, 1969, 528 pp. (In Russ.)  mathscinet  zmath
23. S. I. Mitrokhin, “Asymptotics of eigenvalues of differential operator with alternating weight function”, Russian Mathematics, 62:6 (2018), 27–42  mathnet  mathscinet  zmath
24. R. Bellman, K. L. Cook, Differential-difference equations, Academic Press, London, 1963, 462 pp.
25. V. A. Sadovnichyi, V. B. Lyubishkin, “On some new results in the theory of regularized traces of differential operators”, Differential Equations, 18:1 (1982), 109–116 (In Russ.)  mathnet  mathscinet


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