Ergodic Estimations for Toeplitz Sequences Generated by a Symbol

TL;DR

This paper investigates the convergence properties of ergodic formulas for Toeplitz matrix sequences generated by a symbol, providing explicit bounds based on matrix size and regularity conditions.

Contribution

It offers new explicit bounds on ergodic convergence for Toeplitz matrices depending on matrix size and regularity of the symbol and test functions.

Findings

Derived explicit bounds for ergodic convergence rates

Analyzed the influence of symbol regularity on convergence

Provided practical estimates for Toeplitz matrix sequences

Abstract

We analyse the convergence of the ergodic formula for Toeplitz matrix-sequences generated by a symbol and we produce explicit bounds depending on the size of the matrix, the regularity of the symbol and the regularity of the test function.