On a spectral expansion formula for a class of second order differential equation with discontinuous coefficient

다국어 초록 (Multilingual Abstract)

In this paper the direct scattering problem with the Sturm-Liouville operator on the half line [0,+∞ is investigated. Some spectral properties are given. The resolvent operator is defined. The expansion formula with respect to eigenfunctions is given and equivalence between this formula and Parseval equality is shown.

참고문헌 (Reference)

1 A. A. Darwish, "The inverse scattering problem for a singular boundary value problem" 22 : 37-56, 1993

2 M. G. Gasymov, "The direct and inverse problem of spectral analysis for a class of equations with discontinuous coe cient, Nonclassical Methods in Geophysics" USSR 37-44, 1977

3 B. M. Levitan, "Sturm-Liouville and Dirac Operators" Kluwer Academic Publishers Group 1991

4 V. A. Marchenko, "Sturm-Liouville Operators and Applications" AMS Chelsea Publish-ing 2011

5 S. A. Tikhonov, "On the uniquness of the solution of the problem of electric prospecting" 69 : 797-800, 1949

6 I. M. Guseinov, "On an inverse problem for a second order di erential operator" 57 (57): 597-598, 2002

7 M. A. Naimark, "Linear Di erential Operators" Frederick Ungar Publishing Co. 1967

8 E. C. Titchmarsh, "Eigenfunction Expansions Associated with Second Order Di erential Equations Part I" Clarendon Press 1962