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We study the bounded operators on weighted spaces Lw^2 on R^+ commutingeither with the right translations St or left translations and we establish theexistence of a symbol for these operators. We characterize completely thespectrum of St. We give also a spectral results for the left translations andfor the bounded operators commuting with the semi-group (St) or with thesemi-group of the left translations.

Spectra of translations and Wiener-Hopf operators on Lw^2(R^+)