\input zb-basic
\input zb-ioport
\iteman{io-port 01445612}
\itemau{Gabardo, Jean-Pierre}
\itemti{Hilbert spaces of distributions having an orthogonal basis of exponentials.}
\itemso{J. Fourier Anal. Appl. 6, No.3, 277-298 (2000).}
\itemab
One of the main results is a characterization of the Hilbert spaces consisting of distributions supported on $[0,1]$, for which $\{e^{2\pi i mx}\}_{m\in \Bbb Z}$ is a complete orthonormal system. The results are generalized to spectral pairs, and used to generalize Shannon's sampling theorem.
\itemrv{Ole Christensen (Lyngby)}
\itemcc{}
\itemut{band-limited; sampling; spectral pairs}
\itemli{doi:10.1007/BF02511156}
\end