Graph theoretic uncertainty and feasibility

TL;DR

This paper develops tight bounds for uncertainty principles on graphs, linking eigenfunctions of modified Laplacians to bounds and establishing the feasible region for difference estimators in a two-dimensional space.

Contribution

It introduces a graph-theoretic framework with tight bounds for uncertainty principles and characterizes the feasibility region for difference estimators.

Findings

Eigenfunctions of modified Laplacians determine bounds.

Established the feasibility region in  space.

Provided tight bounds for difference estimators.

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 $\mathbb{R}^2$.