Equality of two spectra arising in harmonic analysis and semigroup theory
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- by Ralph Chill and Eva Fašangová PDF
- Proc. Amer. Math. Soc. 130 (2002), 675-681 Request permission
Abstract:
We show that a new notion of a spectrum of a function $u\in L^\infty ({\mathbb R}_+,X)$ ($X$ is a Banach space), defined by B. Basit and the first author, coincides with the Arveson spectrum of some shift group, provided $u$ is uniformly continuous. We apply this result to prove a new version of a tauberian theorem.References
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Additional Information
- Ralph Chill
- Affiliation: Abteilung Angewandte Analysis, Universität Ulm, 89069 Ulm, Germany
- MR Author ID: 628534
- Email: chill@mathematik.uni-ulm.de
- Eva Fašangová
- Affiliation: Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
- Email: fasanga@karlin.mff.cuni.cz
- Received by editor(s): February 7, 2000
- Received by editor(s) in revised form: August 2, 2000
- Published electronically: June 19, 2001
- Additional Notes: Part of this work was done while the first author visited the Charles University of Prague. He is grateful for the warm hospitality and the financial support. The second author is supported by grant No. 201/98/1450 of the Grant Agency of the Czech Republic, grant No. 166/1999 of the Grant Agency of Charles University, and grant No. CEZ J 13/98113200007.
- Communicated by: David R. Larson
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 675-681
- MSC (2000): Primary 47D03; Secondary 47A10, 40E05
- DOI: https://doi.org/10.1090/S0002-9939-01-06146-9
- MathSciNet review: 1866019