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Isospectral measures
Journal article   Open access  Peer reviewed

Isospectral measures

Dorin Ervin Dutkay and Palle E.T Jorgensen
The Rocky Mountain journal of mathematics, Vol.43(5), pp.1497-1512
2013
DOI: 10.1216/RMJ-2013-43-5-1497
url
https://doi.org/10.1216/RMJ-2013-43-5-1497View
Published (Version of record) Open Access

Abstract

In recent papers a number of authors have considered Borel probability measures $\mu$ in $\br^d$ such that the Hilbert space $L^2(\mu)$ has a Fourier basis (orthogonal) of complex exponentials. If $\mu$ satisfies this property, the set of frequencies in this set are called a spectrum for $\mu$. Here we fix a spectrum, say $\Gamma$, and we study the possibilities for measures $\mu$ having $\Gamma$ as spectrum.

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