Graph theoretic uncertainty and feasibility

Abstract

We expand upon a graph theoretic set of uncertainty principles with tight bounds for difference estimators acting simultaneously in the graph domain and the frequency domain. We show that the eigenfunctions of a modified graph Laplacian and a modified normalized graph Laplacian operator dictate the upper and lower bounds for the inequalities. Finally, we establish the feasibility region of difference estimator values in $\mathbb{R}^2$.