Spectra of translations and Wiener-Hopf operators on Lw^2(R^+)
Violeta Petkova
TL;DR
This paper investigates the spectral properties of translation and Wiener-Hopf operators on weighted L^2 spaces over R^+, establishing symbol existence and characterizing spectra for these operators and their commuting counterparts.
Contribution
It introduces a comprehensive spectral analysis and symbol characterization for translation and Wiener-Hopf operators on weighted L^2 spaces, extending previous results.
Findings
Complete spectrum characterization of right translation operators.
Existence of symbols for bounded operators commuting with translations.
Spectral results for operators commuting with translation semigroups.
Abstract
We study the bounded operators on weighted spaces Lw^2 on R^+ commuting either with the right translations St or left translations and we establish the existence of a symbol for these operators. We characterize completely the spectrum of St. We give also a spectral results for the left translations and for the bounded operators commuting with the semi-group (St) or with the semi-group of the left translations.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Mathematical Analysis and Transform Methods · Holomorphic and Operator Theory