Browsing by Author "El-Raheem, Zaki F. A."
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Item The Eigenfunction Expansion for a Dirichlet Problem with Explosive Factor(HINDAWI PUBLISHING CORPORATION, 2011) El-Raheem, Zaki F. A.; Nasser, A. H.We prove the eigenfunction expansion formula for a Dirichlet problem with explosive factor by two ways, first by standard method and second by proving a convergence in some metric space L(2)(0, pi; rho(x)).Item The equiconvergence of the eigenfunction expansion for a singular version of one-dimensional Schrodinger operator with explosive factor(SPRINGER INTERNATIONAL PUBLISHING AG, 2011) El-Raheem, Zaki F. A.; Nasser, A. H.This paper is devoted to prove the equiconvergence formula of the eigenfunction expansion for some version of Schrodinger operator with explosive factor. The analysis relies on asymptotic calculation and complex integration. The paper is of great interest for the community working in the area.Item On the spectral investigation of the scattering problem for some version of one-dimensional Schrodinger equation with turning point(SPRINGER INTERNATIONAL PUBLISHING AG, 2014) El-Raheem, Zaki F. A.; Nasser, A. H.In this paper we introduce and investigate the eigenvalues and the normalizing numbers as well as the scattering function for some version of the one-dimensional Schrodinger equation with turning point on the half line.Item The Regularized Trace Formula of the Spectrum of a Dirichlet Boundary Value Problem with Turning Point(Hindawi Publishing Corporation, 2012) El-Raheem, Zaki F. A.; Nasser, A. H.We calculate the regularized trace formula of the infinite sequence of eigenvalues for some version of a Dirichlet boundary value problem with turning points.