Spectral singularities of Klein-Gordon s-wave equations with an integral boundary condition

Acta Mathematica Hungarica

Volumn 97, Issue 1-2, 2002, Pages 121-131

  Bairamov, E ^a   Karaman, O ^a  

^a ANKARA UNIVERSITY   (Turkey)

Author keywords

Eigenvalue problems; Klein Gordon equations; Spectral singularities

Indexed keywords

EID: 0036811044     PISSN: 02365294     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020815113773     Document Type: Article

References (21)

1. E. Bairamov, O. Çakar and A.O. Çelebi, Quadratic pencil of Schrödinger operators with spectral singularities: Discrete spectrum and principal functions, J. Math. Anal. Appl., 216 (1997), 303-320.
2. E. Bairamov, O. Çakar and A.M. Krall, Spectrum and spectral singularities of a quadratic pencil of a Schrödinger operator with a general boundary condition, J. Differential Equations, 151 (1999), 252-267.
3. E. Bairamov, O. Çakar and A.M. Krall, An eigenfunction expansion for a quadratic pencil of a Schrödinger operator with spectral singularities, J. Differential Equations, 151 (1999), 268-289.
4. E. Bairamov and A.O. Çelebi, Spectrum and spectral expansion for the non-selfadjoint discrete Dirac operators, Quart. J. Math. Oxford, 50 (1999), 371-384.
5. E. Bairamov and A.O. Çelebi, Spectral properties of the Klein-Gordon s-wave equation with complex potential, Indian J. Pure Appl. Math., 28 (1997), 813-824.
6. E.P. Dolzhenko, Boundary value uniqueness theorems for analytic functions, Math. Notes, 26 (1979), 437-442.
7. M.G. Gasymov, On the decomposition in a series of eigenfunctions for non-selfadjoint boundary value problem of the solution of a differential equation with a singularity at zero point, Soviet Math. Dokl., 6 (1965), 1426-1429.
8. M.G. Gasymov and F.G. Maksudov, The principal part of the resolvent of non-selfadjoint operators in neighbourhood of spectral singularities, Funct. Anal. Appl., 6 (1972), 185-192.
9. W. Greiner, Relativistic Quantum Mechanics. Wave Equations, Springer-Verlag (Berlin/New York, 1994).
10. M. Jaulent and C. Jean, The inverse s-wave scattering problem for a class of potentials depending on energy, Comm. Math. Phys., 28 (1972), 177-220.
11. A.M. Krall, The adjoint of differential operator with integral boundary conditions, Proc. Amer. Math. Soc., 16 (1965), 738-742.
12. A.M. Krall, A nonhomogeneous eigenfunction expansion, Trans. Amer. Math. Soc., 117 (1965), 352-361.
13. A.M. Krall, Nonhomogeneous differential operators, Michigan Math. J., 12 (1965), 247-265.
14. 2, Duke Math. J., 32 (1965), 97-102.
15. A.M. Krall, Second order ordinary differential operators with general boundary conditions, Duke Math. J., 32 (1965), 617-625.
16. A.M. Krall, On the expansion problem for non-selfadjoint ordinary differential operators of second order, Duke Math. J., 34 (1967), 163-174.
17. V.E. Lyance, Expansion in principal functions for an operator with spectral singularities, I, II, Rev., Roum. Math. Puree et Appl., 11 (1966), 921-950, 1187-1224.
18. V.E. Lyance, A Differential Operator with Spectral Singularities I, II, AMS Translations, Ser. 2, Vol. 60 (1967), 185-225, 227-283.
19. V.A. Marchenko, Expansion in Eigenfunctions of Non-selfadjoint Singular Second Order Differential Operators, AMS Translations Ser. 2, Vol. 25 (1963), 77-130.
20. M.A. Naimark, Investigation of the Spectrum and the Expansion in Eigenfunctions of a Non-selfadjoint Operator of Second Order on a Semi-axis, AMS Translations, Ser. 2. Vol. 16 (1960), 103 193.
21. M.A. Naimark, Linear Differential Operators II, Ungar (New York: 1968).