Finite Section Method for a Banach Algebra of Convolution Type Operators on $L^p(\mathbb{R})$ with Symbols Generated by $PC$ and $SO$

TL;DR

This paper demonstrates that the finite section method can be effectively applied to a broad class of convolution-type operators on L^p spaces, generated by piecewise continuous and slowly oscillating symbols.

Contribution

It establishes the applicability of the finite section method to a new class of operators in a Banach algebra generated by specific multiplication and convolution operators.

Findings

Finite section method is applicable to a wide class of convolution operators.

Operators are generated by piecewise continuous and slowly oscillating symbols.

The results extend the scope of numerical methods for operator analysis.

Abstract

We prove the applicability of the finite section method to an arbitrary operator in the Banach algebra generated by the operators of multiplication by piecewise continuous functions and the convolution operators with symbols in the algebra generated by piecewise continuous and slowly oscillating Fourier multipliers on $L^p(\mathbb{R})$, $1<p<\infty$.