Isospectral measures

Details Isospectral measures Isospectral measures

2010-11-05

arxiv.org/abs/1011.1462v3

Mathematics

Functional Analysis

v3

Scientific paper

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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