Abstract:Landscape functions are a popular tool used to provide upper bounds for eigenvectors of Schrödinger operators on domains. We review some known results obtained in the last ten years, unify several approaches used to achieve such bounds, and extend their scope to a large class of linear and nonlinear operators on general Banach lattices. We also use landscape functions to derive lower estimates on spectral gaps and Cheeger constants, as well as upper bounds on heat kernels.Our methods solely rely on order prope… Show more
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