The Whittaker-Kotel'nikov-Shannon theorem, spectral translates and Plancherel's formula (Q1882374)

This paper shows the equivalence of the generalized Plancherel formula, the convolution theorem and the null intersection condition on spectral translates. Moreover, it is proved that the sampling theorem is equivalent to the null intersection condition when the spectrum has finite measure. Finally, the authors investigate a property of the null intersection condition.