Spectra of Bochner-Riesz means on $L^p$

TL;DR

This paper investigates the spectral properties of Bochner-Riesz means on L^p spaces, revealing that their spectra are either the unit interval or the entire complex plane depending on p.

Contribution

It establishes the precise spectral characterization of Bochner-Riesz means on L^p spaces, a significant advancement in understanding their functional analysis properties.

Findings

Spectra are either [0,1] or the entire complex plane.

Spectral behavior depends on the value of p.

Provides a complete spectral description for these operators.

Abstract

The Bochner-Riesz means are shown to have either the unit interval $[0,1]$ or the whole complex plane as their spectra on $L^p, 1\le p<\infty$