논문KCI 등재
On a spectral expansion formula for a class of second order differential equation with discontinuous coefficient
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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.
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 (8)
- A. A. Darwish, "The inverse scattering problem for a singular boundary value problem", New Zealand Journal of Mathematics, 22, pp.37~56 (1993)
- M. G. Gasymov, "The direct and inverse problem of spectral analysis for a class of equations with discontinuous coecient, Nonclassical Methods in Geophysics", pp.37~44 (1977), USSR
- I. M. Guseinov, "On an inverse problem for a second order di erential operator", In Usp. Math. Nauk, 57(3), pp.597~598 (2002)
- B. M. Levitan, "Sturm-Liouville and Dirac Operators" (1991), Kluwer Academic Publishers Group
- V. A. Marchenko, "Sturm-Liouville Operators and Applications" (2011), AMS Chelsea Publish-ing
- M. A. Naimark, "Linear Di erential Operators" (1967), Frederick Ungar Publishing Co.
- S. A. Tikhonov, "On the uniquness of the solution of the problem of electric prospecting", Doklady Akademii Nauk SSSR, 69, pp.797~800 (1949)
- E. C. Titchmarsh, "Eigenfunction Expansions Associated with Second Order Di erential Equations Part I" (1962), Clarendon Press
관련 논문AI추천
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