Formula for Second Regularized Trace of a Problem with Spectral Parameter Dependent Boundary Condition

Year 2011, Volume: 40 Issue: 5, 635 - 647, 01.05.2011

Mehmet Bayramoglu Nigar Aslanova

Keywords

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References

• Albayrak, I., Bayramoglu, M. and Adiguzalov, E. E. The second regularized trace formula for the Sturm-Liowille problem with spectral parameter in a boundary condition, Methods of functional Analysis and Topology 6 (3), 1–8, 2000.
• Aslanova, N. M. A trace formula of one boundary value problem for the Sturm-Liouville operator equation, Siberian Math. J. 49 (6), 1207–1215, 2008.
• Dikii, L. A. On one formula by Gelfand-Levitan, Uspech. Mat. Nauk. 8 (2), 119–123, 1953. [4] Dikii, L. A. A new method of calculation of eigenvalues of Sturm-Liouville operator, Dokl. Akad. Nauk. 116 (1), 12–14, 1957. [5] Dikii, L. A. Trace formulas for Sturm-Liouville differential operators, Uspech. Mathem. Nauk. XIII. 3 (81), 111–143, 1958. [6] Erdal, G. The trace formula for a differential operator of fourth order with bounded operator coefficients and two terms, Turk J. Math. 28, 231–254, 2004.
• Gasymov, M. G. On sum of differences of eigenvalues for two self-adjoint operators, Doclad. AN SSSR. 152 (6), 1202–1205, 1953.
• Gelfand, I. M. and Levitan, B. M. About one simple identity for eigenvalues of second order differential operator, DAN SSSR. 88 (4), 593–596, 1953.
• Gohberg, N. I. and Krein, M. G. Introduction to the Theory of Linear Non-Selfaddjoint Operators in Hilbert Space(“Nauka”, Moscow, 1965).
• Guseynov, G. Sh. and Levitan, B. M. On trace formulas for Sturm-Liouville operator, Vest- nic MGU, Ser. Matem. Mech. 1, 40–49, 1978.
• Hilbert, R. C. and Kramer, V. A. Trace formulas for powers of a Sturm-Lioville operator, Canada J. Math. 16 (4), 412–422, 1964.
• Kato, T. Perturbation Theory for Linear Operators (Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1984).
• Lax, P. D. Trace formulas for the Sch¨odinger operator, Comm. Pure Appl. Math. 47 (4), 503–512, 1994.
• Levitan, B. M. Regularized traces and conditions for smooth periodicity for potential of Sturm-Liouville equation, Sib. Math. J. 22 (2), 137–148, 1980.
• Maksudov, F. G., Bayramoglu, M. and Adigezalov, A. A. On regularized trace of Sturm- Liouvilles operator on finite segment with unbounded operator coefficient, DAN SSSR. 277(4), 795–799, 1984.
• Rybak, M. A. On asymptotic of eigenvalue distribution of some boundary value problems for Sturm-Liouville operator equation, Ukr. Math. J. 32 (2), 248–252, 1980.
• Sadovnichii, V. A. On a trace formula of difference of two ordinary differential operators of high orders, Dif. Urav. 2 (12), 1611–1629, 1966.
• Sadovnichii, V. A. and Podolskii, V. E. Trace of operators with relativly compact perturba- tion, Mat. Sbor. 193 (2), 129–152, 2002.
• Sadovnichii, V. A. and Podolskii, V. E. Trace of operators. Uspech. Matem. Nauk. 61 (5), 89–156, 2006.