Spectral theory for Borel sets in \(\mathbb{R}{}^ n\) of finite measure
A pair \((\Omega,\Lambda)\) with \(\Omega\) and \(\Lambda\) subsets of \({\mathbf R}^ n\) with \(\Omega\) of finite measure is called a spectral pair if the functions \(e^{\lambda\cdot x}\) are an orthonormal basis for \(L^ 2(\Omega)\). It is shown that any spectral pair may be factored in the Cartesian product of a fundamental domain with its dual lattice and a so-called simple factor. Simple factors can be described by certain finite coverings of an associated torus and relations of generated \(C^*\)- algebras.
scientific article; zbMATH DE number 90037
scientific article