Equality of two spectra arising in harmonic analysis and semigroup theory |
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| Authors: | Ralph Chill Eva Fasangová |
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| Institution: | Abteilung Angewandte Analysis, Universität Ulm, 89069 Ulm, Germany ; Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic |
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| 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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| Keywords: | Spectrum of a function Arveson spectrum $C_0$-group Fourier transform tauberian theorem |
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