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Spectra of measures and wandering vectors


Authors: Dorin Ervin Dutkay and Palle E.T. Jorgensen
Journal: Proc. Amer. Math. Soc. 143 (2015), 2403-2410
MSC (2010): Primary 42A32, 05B45, 43A25
DOI: https://doi.org/10.1090/S0002-9939-2015-12656-1
Published electronically: February 6, 2015
MathSciNet review: 3326023
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Abstract: We present a characterization of the sets that appear as Fourier spectra of measures in terms of the existence of a strongly continuous representation of the ambient group that has a wandering vector for the given set.


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Additional Information

Dorin Ervin Dutkay
Affiliation: Department of Mathematics, University of Central Florida, 4000 Central Florida Boulevard, P.O. Box 161364, Orlando, Florida 32816-1364
Email: Dorin.Dutkay@ucf.edu

Palle E.T. Jorgensen
Affiliation: Department of Mathematics, 14 MacLean Hall, University of Iowa, Iowa City, Iowa 52242-1419
Email: jorgen@math.uiowa.edu

DOI: https://doi.org/10.1090/S0002-9939-2015-12656-1
Keywords: Fuglede conjecture, spectrum, unitary one-parameter groups, spectral pairs, locally compact abelian groups, Fourier analysis, wandering vector.
Received by editor(s): September 4, 2012
Published electronically: February 6, 2015
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2015 American Mathematical Society