Tetsuya Takabatake
Published 2022-06-10Version 1
We investigate error orders for integral limit approximations to traces of products of Toeplitz matrices generated by integrable functions on $[-\pi,\pi]$ having some singularities at the origin. Even though a sharp error order of the above approximation is derived in Theorem~2 of \cite{Lieberman-Phillips-2004}, its proof contains an inaccuracy as pointed out by \cite{Ginovyan-Sahakyan-2013}. In the present paper, we reinvestigate the claim given in Theorem~2 of \cite{Lieberman-Phillips-2004} and give an alternative proof of their claim.
Asymptotic of the terms of the Gegenbauer polynomial on the unit circle and applications to the inverse of Toeplitz matrices
Toeplitz matrices for the study of the fractional Laplacian on a bounded interval
On the extension for Toeplitz matrices of certain Markov inequalities
![QR code for arXiv:2209.01616 [math.CA]](http://oss.arxitics.com/images/favicon.svg)