We prove upper bounds estimates for the large time behavior of the heat kernel and for the resolvent of the form Laplacian on Riemannian symmetric spaces, and we obtain L 2+ǫestimates for its resolvent on locally symmetric spaces. We deduce lower bounds for the bottom of the spectrum of the form Laplacian and some results on the vanishing of the L 2 -cohomology of locally symmetric spaces.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.