This paper examines and develops matrix methods to approximate the eigenvalues of a fourth order Sturm-Liouville problem subjected to a kind of fixed boundary conditions, furthermore, it extends the matrix methods for a kind of general boundary conditions. The idea of the methods comes from finite difference and Numerov’s method as well as boundary value methods for second order regular Sturm-L...

Eigenvalues in the essential spectrum of a weighted Sturm-Liouville operator are studied under the assumption that the weight function has one turning point. An abstract approach to the problem is given via a functional model for indefinite Sturm-Liouville operators. Algebraic multiplicities of eigenvalues are obtained. Also, operators with finite singular critical points are considered. MSC-cl...

Gelfand-Graev characters and their degenerate counterparts have an important role in the representation theory of finite groups of Lie type. Using a characteristic map to translate the character theory of the finite unitary groups into the language of symmetric functions, we study degenerate Gelfand-Graev characters of the finite unitary group from a combinatorial point of view. In particular, ...

‎This paper deals with the singular Sturm-Liouville expressions‎ ‎$ ‎ell y =‎ -‎y''+q(x)y=lambda y‎ ‎$‎ ‎on a finite interval‎, ‎where the potential function $q$ is real and‎ ‎has a singularity inside the interval‎. ‎Using the asymptotic estimates of a‎ ‎spectral fundamental system of solutions of Sturm-Liouville‎ ‎equation‎, ‎the asymptotic form of the solution of the‎ ‎equation (0.1) and the ...

In this paper, a Bernoulli pseudo-spectral method for solving nonlinear fractional Volterra integro-differential equations is considered. First existence of a unique solution for the problem under study is proved. Then the Caputo fractional derivative and Riemman-Liouville fractional integral properties are employed to derive the new approximate formula for unknown function of the problem....

Let A be a Banach algebra. We call a pair (G,A) a Gelfand theory for A if the following axioms are satisfied: (G 1) A is a C∗-algebra, and G : A → A is a homomorphism; (G 2) the assignment L 7→ G−1(L) is a bijection between the sets of maximal modular left ideals of A and A, respectively; (G 3) for each maximal modular left ideal L of A, the linear map GL : A/G−1(L) → A/L induced by G has dense...

This thesis gives an introduction to the study of Gelfand pairs and their applications. We begin with a brief introduction to the notion of a Gelfand pair and then move to some of the foundational results concerning Gelfand pairs. Next, we explore specific examples of Gelfand pairs, developing tools of independent interest as we progress. We find that consideration of a specific example of a Ge...

When solving the inverse scattering problem for a discrete Sturm–Liouville operator with a rapidly decreasing potential, one gets reflection coefficients s± and invertible operators I +Hs± , where Hs± is the Hankel operator related to the symbol s±. The Marchenko–Faddeev theorem [8] (in the continuous case, for the discrete case see [4, 6]), guarantees the uniqueness of the solution of the inve...

In this paper, we studied q-analogue of Sturm–Liouville boundary value problem on a finite interval having discontinuity in an interior point. We proved that the q-Sturm–Liouville is self-adjoint modified Hilbert space. investigated spectral properties eigenvalues and eigenfunctions problem. shown are form complete system. Finally, sampling theorem for integral transforms whose kernels basic fu...