Lower bounds on \(\| K^ n \|_{1\to \infty}\) for some contractions \(K\) of \(L^ 2 (\mu)\), with applications to Markov operators
Let \((X, \mu, d)\) be a measured space. Let \(K\) be a selfadjoint contraction on \(L^2 (X, \mu)\), whose kernel \(k(x, y)\) lives on a fixed neighborhood of the diagonal of \(X\times X\). We prove lower bounds on \(|K^n |_{1\to \infty}\), depending on upper bounds on the measure of the balls of \(X\). Applications to Markov operators on groups and graphs are given, as well as a similar result for the heat operator on some Riemannian manifolds with bounded below Ricci curvature.
heat operator on some Riemannian manifolds with bounded below Ricci curvature
scientific article; zbMATH DE number 840207
scientific article