On approximation methods generated by generalized Bochner-Riesz kernels

TL;DR

This paper investigates the convergence properties and approximation accuracy of methods based on generalized Bochner-Riesz kernels, providing sharp results and exact approximation orders in various function spaces.

Contribution

It introduces new sharp convergence results and determines the exact order of approximation for generalized Bochner-Riesz kernel methods.

Findings

Sharp convergence results for generalized Bochner-Riesz means

Exact order of approximation in $K$-functional and $L_p$ spaces

Results applicable to spaces with $0<p<1$

Abstract

Some sharp results related to the convergence of means and families of operators generated by the generalized Bochner-Riesz kernels are obtained. The exact order of approximation of functions by these methods via $K$-functional (or its realization in the case of the space $L_p$, $0<p<1$) is derived.