A discrete variation on Kroneckerʹs theorem Original Research Article

It is a classical therem due to Kronecker that a Hankel operator with bounded measurable symbol on the unit circle has finite rank precisely when the antianalytic part of the symbol is rational. There is a similar result for the Hankel matrices analogously formed from the discrete Fourier transform of a continuous function: namely, that these matrices have uniformly bounded finite rank precisely when the symbol itself is rational.