Group theoretic and geometric properties of multivariable Fourier series (Q1311333)

Let \(\Omega\subseteq \mathbb{R}^ d\) be a measurable subset with finite positive Lebesgue measure. The article investigates the question, when it is possible to find a set \(\Lambda\) such that the exponentials \(\{e^{i\lambda\cdot x}: \lambda\in\Lambda\}\) form an orthogonal basis for the Hilbert space \({\mathcal L}^ 2(\Omega)\). The pair \((\Omega,\Lambda)\) is called a spectral pair. Also the connection between \(\Omega\) and \(\Lambda\) is investigated. Proofs are found in the authors' article in J. Funct. Anal. 107, No. 1, 72-104 (1992; Zbl 0774.42021).