A spectral equivalence for Jacobi matrices

Spectral measures of Jacobi operators with random potentials

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 ...

Comparative study on solving fractional differential equations via shifted Jacobi collocation method

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...

The extended Lotka-Volterra lattice and affine Jacobi varieties of spectral curves

Abstract: Based on the work by Smirnov and Zeitlin, we study a simple realization of the matrix construction of the affine Jacobi varieties. We find that the realization is given by a classical integrable model, the extended Lotka-Volterra lattice. We investigate the integrable structure of the representative for the gauge equivalence class of matrices, which is isomorphic to the affine Jacobi ...

Equivalence Classes of Block Jacobi Matrices

The paper contains two results on the equivalence classes of block Jacobi matrices: first, that the Jacobi matrix of type 2 in the Nevai class has An coefficients converging to 1, and second, that under an L1-type condition on the Jacobi coefficients, equivalent Jacobi matrices of types 1, 2 and 3 are pairwise asymptotic.

Two modified Jacobi methods for M-matrices