Equality of two spectra arising in harmonic analysis and semigroup theory

Authors:
Ralph Chill and Eva Fasangová

Journal:
Proc. Amer. Math. Soc. **130** (2002), 675-681

MSC (2000):
Primary 47D03; Secondary 47A10, 40E05

Published electronically:
June 19, 2001

MathSciNet review:
1866019

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that a new notion of a spectrum of a function ( is a Banach space), defined by B. Basit and the first author, coincides with the Arveson spectrum of some shift group, provided is uniformly continuous. We apply this result to prove a new version of a tauberian theorem.

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Additional Information

**Ralph Chill**

Affiliation:
Abteilung Angewandte Analysis, Universität Ulm, 89069 Ulm, Germany

Email:
chill@mathematik.uni-ulm.de

**Eva Fasangová**

Affiliation:
Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic

Email:
fasanga@karlin.mff.cuni.cz

DOI:
http://dx.doi.org/10.1090/S0002-9939-01-06146-9

Keywords:
Spectrum of a function,
Arveson spectrum,
$C_0$-group,
Fourier transform,
tauberian theorem

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

Article copyright:
© Copyright 2001
American Mathematical Society