Spectra of measures and wandering vectors
Dorin Ervin Dutkay, Palle E.T. Jorgensen
TL;DR
This paper characterizes the Fourier spectra of measures through the existence of a strongly continuous group representation with a wandering vector, linking spectral properties to representation theory.
Contribution
It introduces a novel characterization of Fourier spectra of measures using the concept of wandering vectors in group representations.
Findings
Spectra are characterized via wandering vectors.
Establishes a connection between spectral sets and group representations.
Provides a new perspective on measure spectra in harmonic analysis.
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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Taxonomy
TopicsMathematical Dynamics and Fractals · Mathematical Analysis and Transform Methods · Topological and Geometric Data Analysis