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2013 | 11 | 3 | 561-573
Tytuł artykułu

Multipliers and Wiener-Hopf operators on weighted L p spaces

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Treść / Zawartość
Warianty tytułu
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}.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
3
Strony
561-573
Opis fizyczny
Daty
wydano
2013-03-01
online
2012-12-22
Twórcy
  • Université de Lorraine, LMAM, UMR 7122, Ile du Saulcy, 57045, Metz Cedex 1, France, petkova@univ-metz.fr
Bibliografia
  • [1] Engel K.-J., Nagel R., A Short Course on Operator Semigroups, Universitext, Springer, New York, 2006
  • [2] Fašangová E., Miana P.J., Spectral mapping inclusions for the Phillips functional calculus in Banach spaces and algebras, Studia Math., 2005, 167(3), 219–226 http://dx.doi.org/10.4064/sm167-3-3[Crossref]
  • [3] Gearhart L., Spectral theory for contraction semigroups on Hilbert space, Trans. Amer. Math. Soc., 1978, 236, 385–394 http://dx.doi.org/10.1090/S0002-9947-1978-0461206-1[Crossref]
  • [4] Latushkin Yu., Montgomery-Smith S., Evolutionary semigroups and Lyapunov theorems in Banach spaces, J. Funct. Anal., 1995, 127(1), 173–197 http://dx.doi.org/10.1006/jfan.1995.1007[Crossref]
  • [5] Petkova V., Wiener-Hopf operators on L ω2(ℝ+), Arch. Math. (Basel), 2005, 84(4), 311–324 http://dx.doi.org/10.1007/s00013-004-1167-z[Crossref]
  • [6] Petkova V., Multipliers on Banach spaces of functions on a locally compact abelian group, J. Lond. Math. Soc., 2007, 75(2), 369–390 http://dx.doi.org/10.1112/jlms/jdm002[Crossref]
  • [7] Petkova V., Multipliers on a Hilbert space of functions on R, Serdica Math. J., 2009, 35(2), 207–216
  • [8] Petkova V., Spectral theorem for multipliers on L ω2(ℝ), Arch. Math. (Basel), 2009, 93(4), 357–368 http://dx.doi.org/10.1007/s00013-009-0043-2[Crossref][WoS]
  • [9] Petkova V., Spectra of the translations and Wiener-Hopf operators on L ω2(ℝ+), Proc. Amer. Math. Soc. (in press) [WoS]
  • [10] Ridge W.C., Approximate point spectrum of a weighted shift, Trans. Amer. Math. Soc., 1970, 147(2), 349–356 http://dx.doi.org/10.1090/S0002-9947-1970-0254635-5[Crossref]
  • [11] Rudin W., Fourier Analysis on Groups, Interscience Tracts in Pure and Applied Mathematics, 12, Interscience, New York-London, 1962
  • [12] Weis L., The stability of positive semigroups on L p-spaces, Proc. Amer. Math. Soc., 1995, 123(10), 3089–3094
  • [13] Weis L., A short proof for the stability theorem for positive semigroups on L p(µ), Proc. Amer. Math. Soc., 1998, 126(11), 3253–3256 http://dx.doi.org/10.1090/S0002-9939-98-04612-7[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0139-y
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