Estimates for Green′s Function of the Sturm-Liouville Operator

On Generalization of Sturm-Liouville Theory for Fractional Bessel Operator

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

Sturm-liouville Operator with General Boundary Conditions

We classify the general linear boundary conditions involving u′′, u′ and u on the boundary {a, b} so that a Sturm-Liouville operator on [a, b] has a unique self-adjoint extension on a suitable Hilbert space.

Green’s Function for Regular Sturm-Liouville Problems

On‎ ‎inverse problem for singular Sturm-Liouville operator with‎ ‎discontinuity conditions

‎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...

Spectral analysis of a self-similar Sturm-Liouville operator

In this text we describe the spectral nature (pure point or continuous) of a self-similar Sturm-Liouville operator on the line or the half-line. This is motivated by the more general problem of understanding the spectrum of Laplace operators on unbounded finitely ramified self-similar sets. In this context, this furnishes the first example of a description of the spectral nature of the operator...