1 citations · 1 across the 5 of their papers we have counts for
6 papers
Gaussian upper bounds for averaged heat semigroups on graphs
Christian Rose
Characterizations of pointwise Gaussian upper bounds on graphs with possibly unbounded geometry in terms of localized functional inequalities contain errors depending on the vertex…
Off-diagonal upper heat kernel bounds on graphs with unbounded geometry
Christian Rose
Results regarding off-diagonal Gaussian upper heat kernel bounds on discrete weighted graphs with possibly unbounded geometry are summarized and related. After reviewing uniform up…
Optimal Poincaré-Hardy-type Inequalities on Manifolds and Graphs
Florian Fischer, Christian Rose
We review a method to obtain optimal Poincaré-Hardy-type inequalities on the hyperbolic spaces, and discuss briefly generalisations to certain classes of Riemannian manifolds. Afte…
Spectral comparison results for Laplacians on discrete graphs
Patrizio Bifulco, Joachim Kerner, Christian Rose
In the recent literature, various authors have studied spectral comparison results for Schrödinger operators with discrete spectrum in different settings including Euclidean domain…
Gaussian upper heat kernel bounds and Faber-Krahn inequalities on graphs
Christian Rose
We investigate the equivalence of relative Faber-Krahn inequalities and the conjunction of Gaussian upper heat kernel bounds and volume doubling on large scales on graphs. For the…
Gaussian upper bounds, volume doubling and Sobolev inequalities on graphs
Matthias Keller, Christian Rose
We investigate the equivalence of Sobolev inequalities and the conjunction of Gaussian upper heat kernel bounds and volume doubling on large scales on graphs. For the normalizing m…