Paper title: |
On Two-Fold Expansion Formulas For A Singular Sturm-Liouville Operator |
DOI: | https://doi.org/10.4316/JACSM.201902007 |
Published in: | Issue 2, (Vol. 13) / 2019 |
Publishing date: | 2019-12-16 |
Pages: | 45-49 |
Author(s): | ALA Volkan, MAMEDOV Khanlar R. |
Abstract. | In this paper, a singular Sturm-Liouville problem dependent spectral parameter in boundary condition is considered. Special solutions and scattering datas are defined. The resolvent operator is constructed and two-fold spectral expansion formulas in terms of scattering datas are obtained by using Titchmarsh method |
Keywords: | Eigenfunctions, Expansion Formula, Resolvent Operator, Scattering Data |
References: | 1. Allahverdiev B.P., Tuna H., Eigenfunction Expansion for Singular Sturm-Liouville Problems with Transmission Conditions, ElectronicJournal of Diff. Equations,Vol. 2019, No. 03, pp. 1--10, ISSN: 1072-6691, 2019. 2. Bairamov E., Çelebi A.O., Spectral Analysis of Nonselfadjoint Schrödinger Operator with Spectral Parameter in Boundary Conditions, Facta Universitatis (NIS), Serbian Math. Inform.,13, 79-94, 1998. 3. Bairamov E., Yokuş N., Spectral Singularities of Sturm-Liouville Problems with Eigenvalue-Dependent Boundary Conditions, Abstract and Applied Analysis Volume 2009, Article ID 289596, 8 pages, 2009. 4. Cohen D.S., An Integral Transform Associated with Boundary Conditions Containing an Eiganvalue Parameter, SIAM Journal on Applied Mathematics, Vol. 14, No.5, 1164-1175,1966. 5. Freiling G., Yurko V.A., Lectures on Differential Equations of Mathematical Physcis, A First Course UK Edition, 2009. 6. Fulton C.T., Two-Point Boundary Value Problems with Eigenvalue Parameter Contained in the Boundary Conditions, Proceedings of the Royal Society of Edinburgh, Section A 1977, 77 (3-4): 293-308. 7. Fulton C.T., Singular Eigenvalue Problems with Eigenvalue Parameter Contained in the Boundary Conditions, Proceedings of the Royal Society of Edinburgh, Vol. 87, Issue 1-2, pp. 1-34, 1980. 8. Gekhtman M.M and Stankevich I.V., On a Boundary Problem Generated by a Self-adjoint Sturm-Liouville Differential Operator on the Entire Real Axis, Math.Notes, Volume 6,Issue 6,1969. 9. Kravickii A.O., Double Expansion into Series of Eigenfunctions of a Certain Non-Selfadjoint Boundary Value Problem, Diff.Uravneniya, 4, 165-177, 1968. 10. Levitan B.M., Inverse Sturm-Liouville Problems, VSP, Zeist,The Netherlands; 1987. 11. Maksudov F.G., Expansion in Eigenfunctions of Non-Selfadjoint Singular Second-Order Differential Operators Depending on a Parameter, Dokl. Akad. Nauk SSSR, 153, no 5, 1001-1004, 1963. 12. Marchenko V.A., Sturm-Liouville Operators and Their Applications, AMS Chelsea Publishing, 2011. 13. Mamedov Kh.R., Menken H., On the Inverse Problem of the Scattering Theory for a Boundary Value Problem of the Second-Order, North-Holland Math. Stud,197, 185-194, 2004. 14. Mamedov Kh. R., Uniqueness of the Solution of the Inverse Problem of Scattering Theory for the Sturm-Liouville Operator with a Spectral Parameter in the Boundary Condition, Math. Notes, 74, 136-140, 2003. 15. Mamedov Kh.R., Spectral Expansion Formula for a Discontinuous Sturm-Liouville Operator, Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 40, 2014. 16. Naimark M.A., Linear Differential Operators, Frederick Ungar Publishing, 1967. 17. Pocheykina-Fedotova E.A., On the Inverse Problem of Boundary Problem for Second Order Differential Equation on the Half Line,Izvestiya Vuzov, 17: 75-84,1972. 18. Regge T., Analytic Properties of The Scattering Matrix, Nuovo Cimento, 8:671-679, 1958. 19. Regge T.,Construction of Potentials from Resonance Parameters, Nuovo Cimento, 9:491-503, 1958. 20. Titchmarsh, Edward C, Eigenfunction Expansions Associated with Second-Order Differential Equations, Oxford Clarendon Press, 1958. 21. Yurko V.A., On the Reconstruction of the Pencils of Differential Operators on the Half-line, Mathematical Notes,67(2):261-265,2000. 22. Yurko V.A., An Inverse Problem for Pencils of Differential Operators, Sbornik Mathematics,191(10): 1561-1586, 2000.
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