Equivalence classes of block Jacobi matrices

TL;DR

This paper investigates the properties of block Jacobi matrices, showing convergence of coefficients and asymptotic equivalence under certain conditions, thereby advancing understanding of their classification and behavior.

Contribution

It establishes convergence of A_n coefficients for type 2 Jacobi matrices in the Nevai class and proves asymptotic equivalence among different types under L1 conditions.

Findings

A_n coefficients of type 2 Jacobi matrices in the Nevai class converge to 1

Equivalent Jacobi matrices of types 1, 2, and 3 are pairwise asymptotic under L1 conditions

Provides new insights into the classification and asymptotic behavior of block Jacobi matrices

Abstract

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 A_n coefficients converging to 1, and second, that under an L1-type condition on the Jacobi coefficients, equivalent Jacobi matrices of type 1, 2 and 3 are pairwise asymptotic.