Localization of the spectra of dual frames multipliers

TL;DR

This paper investigates the spectral properties of dual frames multipliers in Hilbert spaces, aiming to identify regions in the complex plane where their spectra are contained, based on frame and symbol information.

Contribution

It provides new results on the localization of spectra of dual frames multipliers, enhancing understanding of their spectral behavior in relation to frame and symbol properties.

Findings

Identifies regions in the complex plane containing the spectra

Provides criteria for spectral localization based on frame and symbol data

Enhances spectral analysis of dual frames multipliers

Abstract

This paper concerns dual frames multipliers, i.e. operators in Hilbert spaces consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames, respectively. The goal of the paper is to give some results about the localization of the spectra of dual frames multipliers, i.e. to individuate regions of the complex plane containing the spectra using some information about the frames and the symbols.