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The determinants of dissipative Sturm-Liouville operators with transmission conditions. (English) Zbl 1217.34129
Summary: We study the determinant of perturbation connected with the dissipative operator L generated in L 2 (I). Then using Livšic’s theorem, we investigate the problem of completeness of the system of eigenfunctions and associated functions of L.
MSC:
34L10Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions (ODE)
47E05Ordinary differential operators
References:
[1]Coddington, E. A.; Levinson, N.: Theory of ordinary differential equations, (1955) · Zbl 0064.33002
[2]Naimark, M. A.: Linear differential operators II, (1968)
[3]E.C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations, Oxford, 1946. · Zbl 0061.13505
[4]Everitt, W. N.; Knowles, I. W.; Read, T. T.: Limit-point and limit-circle criteria for Sturm–Liouville equations with intermittently negative principal coefficients, Proc. roy. Soc. Edinburgh sect. A 103, 215-228 (1986) · Zbl 0635.34021 · doi:10.1017/S0308210500018874
[5]Sun, J.; Wang, A.; Zettl, A.: Two-interval Sturm–Liouville operators in direct sum spaces with inner product multiples, Results math. 50, 155-168 (2007) · Zbl 1148.34024 · doi:10.1007/s00025-006-0241-1
[6]Tunç, E.; Mukhtarov, O. Sh.: Fundamental solutions and eigenvalues of one boundary-value problem with transmission conditions, Appl. math. Comput. 157, 347-355 (2004) · Zbl 1060.34007 · doi:10.1016/j.amc.2003.08.039
[7]Akdoğan, Z.; Demirci, M.; Mukhtarov, O. Sh.: Green function of discontinuous boundary-value problem with transmission conditions, Math. methods appl. Sci. 30, 1719-1738 (2007) · Zbl 1146.34061 · doi:10.1002/mma.867
[8]Krall, A. M.; Zettl, A.: Singular self-adjoint Sturm–Liouville problems II: Interior singular points, SIAM J. Math. anal. 19, 1135-1141 (1988) · Zbl 0682.34019 · doi:10.1137/0519078
[9]Fulton, C. T.: Parametrization of titchmarsh’s m(λ)-functions in the limit circle case, Trans. amer. Math. soc. 229, 51-63 (1977) · Zbl 0358.34021 · doi:10.2307/1998499
[10]Guseinov, G. Sh.; Tuncay, H.: The determinants of perturbation connected with a dissipative Sturm–Liouville operators, J. math. Anal. appl. 194, 39-49 (1995) · Zbl 0836.34027 · doi:10.1006/jmaa.1995.1285
[11]Gasymov, M. G.; Guseinov, G. Sh.: Uniqueness theorems for inverse spectral analysis problems for Sturm–Liouville operators in the Weyl limit-circle case, Differ. equ. 25, 394-402 (1989) · Zbl 0702.34018
[12]Wang, Z.; Wu, H.: The completeness of eigenfunctions of perturbation connected with Sturm–Liouville operators, J. syst. Sci. complex. 19, 1-12 (2006) · Zbl 1139.34024 · doi:10.1007/s11424-006-0527-0
[13]Bairamov, E.; Krall, A. M.: Dissipative operators generated by the Sturm–Liouville expression in the Weyl limit circle case, J. math. Anal. appl. 254, 178-190 (2001) · Zbl 0979.34059 · doi:10.1006/jmaa.2000.7233
[14]Krall, A. M.; Zettl, A.: Singular self-adjoint Sturm–Liouville problems, J. differential integral equations 1, 423-432 (1988) · Zbl 0723.34023
[15]Gohberg, I. C.; Krein, M. G.: Introduction to the theory of linear nonselfadjoint operators, (1969) · Zbl 0181.13504