The aim of this paper is to prove new uncertainty principles for integral operators with bounded kernel for which there is a Plancherel Theorem. The first of these results is an extension of Faris’s local uncertainty principle which states that if a nonzero function $f\in L²({ℝ}^d,\mu )$ is highly localized near a single point then (f) cannot be concentrated in a set of finite measure. The second result extends the Benedicks-Amrein-Berthier uncertainty principle and states that a nonzero function $f\in L²({ℝ}^d,\mu )$ and its integral...

For any 0 < ϵ < 1, p ≥ 1 and each function $f\in L^p[0,1]$ one can find a function $g\in L^{\infty }[0,1)$ with mesx ∈ [0,1): g ≠ f < ϵ such that its greedy algorithm with respect to the Walsh system converges uniformly on [0,1) and the sequence $|c_k\left(g\right)|:k\in spec\left(g\right)$ is decreasing, where $c_k\left(g\right)$ is the sequence of Fourier coefficients of g with respect to the Walsh system.