Browsing by Author "Veliev, Oktay A."
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An algorithm for finding the periodic potential of the threedimensional Schrodinger operator from spectral invariants
Veliev, Oktay A. (IOP Publishing, 20110415)In this paper, we investigate the threedimensional Schrodinger operator with a periodic, relative to a lattice Omega of R(3), potential q. A special class V of the periodic potentials is constructed, which is easily and ... 
Asymptotic analysis of non  self  adjoint Hill operators
Veliev, Oktay A. (Springer Verlag, 201312)We obtain uniform asymptotic formulas for the eigenvalues and eigenfunctions of the SturmLiouville operators L (t) (q) with a potential q a L (1)[0,1] and tperiodic boundary conditions, t a (pi, pi]. Using these formulas, ... 
Asymptotic and numerical methods in estimating eigenvalues
Yıldız, Güldem; Yılmaz, Bülent; Veliev, Oktay A. (Hindawi Publishing Corporation, 2013)Asymptotic formulas and numerical estimations for eigenvalues of SturmLiouville problems having singular potential functions, with Dirichlet boundary conditions, are obtained. This study gives a comparison between the ... 
Asymptotic formulae for the Bloch eigenvalues near planes of diffraction
Veliev, Oktay A. (Elsevier, 200612)In this paper we obtain asymptotic formulae of arbitrary order for the Bloch eigenvalue of the periodic Schrödinger operator △ + q(x), of arbitrary dimension, when the corresponding quasimomentum lies near planes of diffraction. 
Asymptotic formulae for the Schrodinger operator with Dirichlet and Neumann boundary conditions
Karakılıç, Sedef; Atılgan, Şirin; Veliev, Oktay A. (Elsevier, 200504)In this paper, we consider the Schrodinger operators defined by the differential expression Lu = Delta u+q(x)u in ddimensional parallelepiped F, with the Dirichlet and Neumann boundary conditions, and obtain the asymptotic ... 
Asymptotic formulas for Dirichlet boundary value problems
Veliev, Oktay A.; Yılmaz, Bülent (Akademiai Kiado, 200505)In this article we obtain asymptotic formulas of arbitrary order for eigenfunctions and eigenvalues of the nonselfadjoint SturmLiouville operators with Dirichlet boundary conditions, when the potential is a summable ... 
Asymptotic formulas for the resonance eigenvalues of the Schrödinger operator
Karakılıç, Sedef; Veliev, Oktay A.; Atılgan, Şirin (TÜBİTAK, 2005)In this paper, we consider the Schrödinger operators defined by the differential expression ... in ddimensional paralellepiped F, with the Dirichlet and the Neumann boundary conditions, where q(x) is a real valued function ... 
Asymptotic formulas with arbitrary order for nonseleadjoint differential operators
Duman, Melda; Kıraç, Alp Arslan; Veliev, Oktay A. (Akademiai Kiado, 200709)We obtain asymptotic formulas with arbitrary order of accuracy for the eigenvalues and eigenfunctions of a nonselfadjoint ordinary differential operator of order n whose coefficients are Lebesgue integrable on [0,1] and ... 
Asymptotically spectral periodic differential operators
Veliev, Oktay A. (MAIK Nauka/Interperiodica, 201809)In this paper, we investigate spectral expansion for the asymptotically spectral differential operators generated in L2m (−∞,∞) by ordinary differential expressions of arbitrary order with periodic matrixvalued coefficients. 
Essential spectral singularities and the spectral expansion for the hill operator
Veliev, Oktay A. (American Institute of Mathematical Sciences, 201711)In this paper we investigate the spectral expansion for the onedimensional Schrodinger operator with a periodic complexvalued potential. For this we consider in detail the spectral singularities and introduce new concepts ... 
Isospectral mathieu  hill operators
Veliev, Oktay A. (Springer Verlag, 201308)In this paper we prove that the spectra of the MathieuHill Operators with potentials ae(i2 pi x) +be (i2 pi x) and ce(i2 pi x) +de (i2 pi x) , where a, b, c and d are complex numbers, are the same if and only if ab = ... 
Multidimensional periodic Schrödinger operator: Perturbation theory and applications
Veliev, Oktay A. (Springer, 2015)The book describes the direct problems and the inverse problem of the multidimensional Schrödinger operator with a periodic potential. This concerns perturbation theory and constructive determination of the spectral ... 
Nonselfadjoint sturm–liouville operators with matrix potentials
Veliev, Oktay A. (Pleiades Publishing, 2007)We obtain asymptotic formulas for nonselfadjoint operators generated by the Sturm–Liouville system and quasiperiodic boundary conditions. Using these asymptotic formulas, we obtain conditions on the potential for which ... 
On Hill's operator with a matrix potential
Veliev, Oktay A. (Wiley, 20080901)In this article we obtain asymptotic formulas for eigenvalues and eigenfunctions of the selfadjoint operator generated by a system of SturmLiouville equations with summable coefficients and quasiperiodic boundary conditions. ... 
On nonselfadjoint sturmliouville operators in the space of vector functions
Şeref, Fulya; Veliev, Oktay A. (MAIK Nauka/Interperiodica, 2014)In this article we obtain asymptotic formulas for the eigenvalues and eigenfunctions of the nonselfadjoint operator generated in L2(m) [0, 1] by the SturmLiouville equation with m x m matrix potential and the boundary ... 
On the basis property of the root functions of differential operators with matrix coefficients
Veliev, Oktay A. (Springer Verlag, 201106)We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and periodic or antiperiodic boundary conditions. Then ... 
On the basis property of the root functions of differential operators with matrix coefficients
Veliev, Oktay A. (Moscow State University, 2009)We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and periodic or antiperiodic boundary conditions. Then ... 
On the basis property of the root functions of some class of nonselfadjoint sturmliouville operators
Nur, Cemile; Veliev, Oktay A. (Springer, 20140315)We obtain the asymptotic formulas for the eigenvalues and eigenfunctions of the SturmLiouville operators with some regular boundary conditions. Using these formulas, we find sufficient conditions on the potential q such ... 
On the basis property of the root functions of Sturm–Liouville operators with general regular boundary conditions
Nur, Cemile; Veliev, Oktay A. (Independent University of Moscow, 201507)We obtain the asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm–Liouville operators with general regular boundary conditions. Using these formulas, we find sufficient condi tions on the potential q ... 
On the constructive determination of spectral invariants of the periodic Schrodinger operator with smooth potentials
Veliev, Oktay A. (IOP Publishing, 20080912)In this paper, we develop the asymptotic formulae, obtained in my previous papers, for the band functions and the Bloch functions of the Schrodinger operator with the smooth periodic potentials. Then using these formulae, ...