THE FOURIER TRANSFORM OF THE CHARACTERISTIC FUNCTION OF A SET, VANISHING ON AN INTERVAL
Pavel Kargaev · Mathematics of the USSR-Sbornik · 1983
A set E with 0 < meas E < +∞ is constructed for which the Fourier transform of its characteristic function vanishes on an interval. The set is the union of a sequence of intervals whose lengths can be estimated asymptotically above and below. The construction is based on an infinite-dimensional version of the implicit function theorem. Bibiography: 6 titles.