We study spectrum inclusion regions for complex Jacobi matrices which are compact perturbations of real periodic Jacobi matrix. The condition sufficient for the lack of discrete spectrum for such matrices is given.

Abstract A joint algebraic interpretation of the biorthogonal Askey polynomials on unit circle and orthogonal Jacobi is offered. It ties their bispectral properties to an algebra called meta-Jacobi $m\mathfrak {J}$ .

This paper pursues obtaining Jacobi spectral collocation methods to solve Caputo fractional differential equations numerically. We used the shifted Jacobi–Gauss–Lobatto or Jacobi–Gauss–Radau quadrature nodes as points and derived differentiation matrices for derivatives. With matrices, were transformed into linear systems, which are easier solve. Two types of numerical simulations, results demo...

Let Hω be a self-adjoint Jacobi operator with a potential sequence {ω(n)}n of independently distributed random variables with continuous probability distributions and let μωφ be the corresponding spectral measure generated by Hω and the vector φ. We consider sets A(ω) which are independent of two consecutive given entries of ω and prove that μωφ(A(ω)) = 0 for almost every ω. This is applied to ...

We present a new oscillation criterion to determine whether the number of eigenvalues below the essential spectrum of a given Jacobi operator is finite or not. As an application we show that Kenser’s criterion for Jacobi operators follows as a special case.

Let x : M → Sn+1(1) be an n-dimensional compact hypersurface with constant scalar curvature n(n − 1)r, r ≥ 1, in a unit sphere Sn+1(1), n ≥ 5, and let Js be the Jacobi operator of M . In 2004, L. J. Aĺıas, A. Brasil and L. A. M. Sousa studied the first eigenvalue of Js of the hypersurface with constant scalar curvature n(n− 1) in Sn+1(1), n ≥ 3. In 2008, Q.-M. Cheng studied the first eigenvalue...