Multipliers and Wiener-Hopf operators on weighted L^p spaces

TL;DR

This paper investigates the spectral properties of multipliers and Wiener-Hopf operators on weighted L^p spaces, establishing the existence of symbols and characterizing spectra for operators commuting with translation operators.

Contribution

It provides a complete characterization of the spectrum of translation operators and their associated Wiener-Hopf operators on weighted L^p spaces, including symbol existence.

Findings

Spectrum of St is fully characterized.

Spectral results for operators commuting with translations are obtained.

Existence of symbols for operators commuting with translations is established.

Abstract

We study the operators T on the weighted space L^p commuting either with the right translations St or left translations P^+S_{-t} and we establish the existence of a symbol of T. We characterize completely the spectrum of St. We obtain a similar result for the spectrum of P^+S_{-t} and some spectral results for the bounded operators commuting with (St), t>0 or with (P^+St), t<0.