Mapping-based uncertainty relations for periodic functions

Abstract

Based on five different mappings of a function on a circle (i.e. a periodic function) to a function on a line or a line segment (i.e. a non-periodic function), measures for the width of a periodic function (expressed in terms of centered second-order moments) are studied, and the associated uncertainty relations are derived, using a generalized version of the Cauchy-Schwarz inequality.