In this paper we investigate a Sturm–Liouville eigenvalue problem on time scales. Existence of the eigenvalues and eigenfunctions is proved. Mean square convergent and uniformly convergent expansions in the eigenfunctions are established. AMS subject classification: 34L10.

on a special interval. We obtain some nodal parameters like nodal points and nodal lengths. In addition, we reconstruct the potential function by nodal points. Results obtained in this paper are similar to the classical Sturm–Liouville problem. However, equations of this type are considered with the condition defined at the origin. We solve the problem on the interval [1,a], that problem is not...

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...

This extended abstract is a summary of the main results in [4]. We consider a stability result for the inverse problem associated with the Sturm-Liouville equation −y′′ + q0(x)y = λy, x ∈ (0, 1), in which the potential q0 ∈ L(0, 1) is allowed to be complex-valued and the spectral data consists of the firstN Dirichlet-Dirichlet eigenvalues and the firstN Dirichlet-Neumann eigenvalues, determined...

‎In this manuscript‎, ‎we study various by uniqueness results for inverse spectral problems of Sturm--Liouville operators using three spectrum with a finite number of discontinuities at interior points which we impose the usual transmission conditions‎. ‎We consider both the cases of classical Robin and eigenparameter dependent boundary conditions.

This study is on the fuzzy eigenvalues and fuzzy eigenfunctions of the Sturm-Liouville fuzzy problem with fuzzy eigenvalue parameter. We find fuzzy eigenvalues and fuzzy eigenfunctions of the problem under the approach of Hukuhara differentiability. We solve an example. We draw the graphics of eigenfunctions. We show that eigenfunctions are valid fuzzy functions or not.

The generalized Fourier transform associated with a selfadjoint Sturm–Liouville operator is a unitary transformation which converts the action of this operator into a simple product by a spectral variable. For a particular operator defined on the half-line and which involves a step function, we show how to extend such a transformation to generalized functions, or distributions, with a suitable ...

Inverse spectral problems consist in recovering operators from their spectral characteristics. Such problems play an important role in mathematics and have many applications in natural sciences (see, for example, [1 – 6]). In 1988, the inverse nodal problem was posed and solved for Sturm-Liouville problems by J. R. McLaughlin [7], who showed that the knowledge of a dense subset of nodal points ...