Results 1 to 10 of about 28 (28)

On unbounded commuting Jacobi operators and some related issues

Concrete Operators, 2019
We consider the situations, when two unbounded operators generated by infinite Jacobi matrices, are self-adjoint and commute. It is found that if two Jacobi matrices formally commute, then two corresponding operators are either self-adjoint and commute ...
Osipov Andrey
doaj   +1 more source

On the completely indeterminate case for block Jacobi matrices

Concrete Operators, 2017
We consider the infinite Jacobi block matrices in the completely indeterminate case, i. e. such that the deficiency indices of the corresponding Jacobi operators are maximal.
Osipov Andrey
doaj   +1 more source

Construction of the spectral expansion for singular β-Sturm-Liouville operators with certain applications

Demonstratio Mathematica
In this paper, we investigate the β −Sturm-Liouville problem within the framework of a generalized quantum difference calculus, which extends Hahn’s difference operator to the half-line.
Koşar Nida Palamut, Koşar Cem
doaj   +1 more source

Existence, Uniqueness, Stability, and Numerical Solution of Second‐Order Quantum Difference Equations: A General Approach via the Riccati Method and Chebyshev Collocation

Journal of Mathematics, Volume 2026, Issue 1, 2026.
In this paper, we investigate the stability and numerical solution of second‐order linear nonhomogeneous equations with the general quantum B‐difference operator. We prove Hyers–Ulam stability (HU s) and Hyers–Ulam–Rassias stability (HUR s) for these equations using a Riccati equation approach and variation of parameters technique.
Karima M. Oraby, Amna Mohamed, Youssri Hassan Youssri, Smritijit Sen   +3 more
wiley   +1 more source

Higher Order Multi-Series Arising from Generalized Alpha-Difference Equation

, 2015
In this paper, the authors extend the theory and m−series of the generalized difference equation to m(α)−series of its α−difference equation. We also investigate the complete and summation solutions of α-difference equation.
S India, B Govindan, Tamil Nadu, G Britto, Antony Xavier, S U Vasantha Kumar   +5 more
core  

A study of ∇-discrete fractional calculus operator on the radial Schrodinger equation for some physical potentials

, 2017
The fractional calculus includes concepts of integrals and derivatives of any complex or real order. The fractional calculus is as old as the usual calculus.
Ozturk, Okkes
core  

On the determinacy of complex Jacobi matrices

, 2002
The aim of this paper is to explore to which extend the theory of the Hamburger moment problem for real Jacobi matrices generalizes to the case of complex Jacobi matrices.
B. Beckermann, M. Castro
core  

Absolutely Continuous Spectrum of One-Dimensional Schrödinger Operators and Jacobi Matrices with Slowly Decreasing Potentials

, 1996
We prove that for any one-dimensional Schrodinger operator with potential V (x) satisfying decay condition jV (x)j Cx \Gamma3=4\Gammaffl ; the absolutely continuous spectrum fills the whole positive semi-axis.
Alexander Kiselev
core  

Asymptotic iteration method for solving Hahn difference equations. [PDF]

Adv Differ Equ, 2021
MacQuarrie L, Saad N, Islam MS.
europepmc   +1 more source

On homogeneous second order linear general quantum difference equations. [PDF]

J Inequal Appl, 2017
Faried N, Shehata EM, El Zafarani RM.
europepmc   +1 more source