Quadrature formulas on graphs

Isaac Pesenson

Session: General

Keywords: combinatorial graphs, combinatorial Laplace operators, cubature formulas on graphs, frames, Poincare ́ and Plancherel-Polya-type inequalities

TL;DR: Developing uadrature formulas with positive coefficients on combinatorial graphs

Abstract:

We consider a disjoint cover (partition) of an undirected weighted finite graph $G$ by $|J|$ connected subgraphs (clusters)
$ \{S_{j}\}$, $j\in J$, and select a function $ \psi_{j}\geq 0 $ on each of the clusters. For a given signal $f$ on $G$ its weighted average samples are defined via inner products $\{\langle \psi_{j}, f\rangle\}_{j\in J} $. The goal of the paper is to describe subspaces of bandlimited functions for which there exist quadrature formulas with positive coefficients based on weighted average samples.

Submission Number: 45