We consider the Sturm-Liouville operator Lu = u ′′ − q(x)u defined on (0, π) with regular but not strongly regular boundary conditions. Under some supplementary assumptions we prove that the set of potentials q(x) that ensure an asymptotically multiple spectrum is everywhere dense in L 1 (0, π). In the present paper we consider eigenvalue problems for the Sturm-Liouville equation u ′′ − q(x)u +...

In this study, we establish a Parseval equality and an expansion formula for a Sturm– Liouville operator on semi-unbounded time scales. AMS subject classification: 34L10.

We study the Al-Salam–Chihara polynomials when q > 1. Several solutions of the associated moment problem are found, and the orthogonality relations lead to explicit evaluations of several integrals. The polynomials are shown to have raising and lowering operators and a second order operator equation of Sturm-Liouville type whose eigenvalues are found explicitly. We also derive new measures with...

We study a restriction of the Hilbert transform as an operator HT from L (a2, a4) to L(a1, a3) for real numbers a1 < a2 < a3 < a4. The operator HT arises in tomographic reconstruction from limited data, more precisely in the method of differentiated back-projection (DBP). There, the reconstruction requires recovering a family of one-dimensional functions f supported on compact intervals [a2, a4...

In this paper we investigate discrete spectrum of the non-selfadjoint matrix Sturm-Liouville operator L generated in L (R+, S) by the differential expression ` (y) = −y +Q (x) y , x ∈ R+ : [0,∞) , and the boundary condition y′ (0)− ( β0 + β1λ+ β2λ 2 ) y (0) = 0 where Q is a non-selfadjoint matrix valued function. Also using the uniqueness theorem of analytic functions we prove that L has a fini...

‎In this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular Sturm-Liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎Also Weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

In this paper we apply the Homotopy perturbation method to derive the higher-order asymptotic distribution of the eigenvalues and eigenfunctions associated with the linear real second order equation of Sturm-liouville type on $[0,pi]$ with Neumann conditions $(y'(0)=y'(pi)=0)$ where $q$ is a real-valued Sign-indefinite number of $C^{1}[0,pi]$ and $lambda$ is a real parameter.

‎in this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular sturm-liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎also weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

in this paper, we investigate the canonical property of solutions of a system of differentialequations having a singularity and turning point of even order. first, by a replacement, we transform thesystem to the sturm-liouville equation with a turning point. using the asymptotic estimates for a specialfundamental system of solutions of sturm-liouville equation, we study the infinite product rep...

This paper [1] has been retracted as it is essentially identical in content with the published article " Determination of Sturm-Liouville operator on a three-star graph from four spectra, " by Dehghani Tazehkand and Akbarfam, published in Acta