Uncertainty principle for vector-valued functions

Abstract

<abstract><p>The uncertainty principle for vector-valued functions of $ L^2({\mathbb{R}}^n, {\mathbb{R}}^m) $ with $ n\ge 2 $ are studied. We provide a stronger uncertainty principle than the existing one in literature when $ m\ge 2 $. The phase and the amplitude derivatives in the sense of the Fourier transform are considered when $ m = 1 $. Based on these definitions, a generalized uncertainty principle is given.</p></abstract>