Hilbert spaces of distributions having an orthogonal basis of exponentials
One of the main results is a characterization of the Hilbert spaces consisting of distributions supported on \([0,1]\), for which \(\{e^{2\pi i mx}\}_{m\in \mathbb Z}\) is a complete orthonormal system. The results are generalized to spectral pairs, and used to generalize Shannon's sampling theorem.
scientific article; zbMATH DE number 1445612