Multipliers and Wiener-Hopf operators on weighted L p spaces

• Autorzy: Violeta Petkova
• Języki publikacji: EN

Abstrakty

EN

We study multipliers M (bounded operators commuting with translations) on weighted spaces L ω p (ℝ), and establish the existence of a symbol µM for M, and some spectral results for translations S t and multipliers. We also study operators T on the weighted space L ω p (ℝ+) commuting either with the right translations S t , t ∈ ℝ+, or left translations P +S −t , t ∈ ℝ+, and establish the existence of a symbol µ of T. We characterize completely the spectrum σ(S t ) of the operator S t proving that $\sigma (S_t ) = \{ z \in \mathbb{C}:|z| \leqslant e^{t\alpha _0 } \} ,$ where α 0 is the growth bound of (S t )t≥0. A similar result is obtained for the spectrum of (P +S −t ), t ≥ 0. Moreover, for an operator T commuting with S t , t ≥ 0, we establish the inclusion [...] , where \(\mathcal{O}\) = {z ∈ ℂ: Im z α 0}.

Słowa kluczowe

EN

Mutilpliers; Semi-groups of translations; Spectrum of translation; Weiner-Hopf operators

Kategorie tematyczne

• 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
• 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 3
• Strony: 561-573

Daty

wydano

2013-03-01

online

2012-12-22

Twórcy

autor

Violeta Petkova

• Université de Lorraine, LMAM, UMR 7122, Ile du Saulcy, 57045, Metz Cedex 1, France

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0139-y