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math.AP2022
Anchored heat kernel upper bounds on graphs with unbounded geometry and anti-trees
Matthias Keller, Christian Rose
We derive Gaussian heat kernel bounds on graphs with respect to a fixed origin for large times under the assumption of a Sobolev inequality and volume doubling on large balls. The…
math.AP2022★ 9 cited
Optimal Hardy Inequality for Fractional Laplacians on the Integers
Matthias Keller, Marius Nietschmann
We study the fractional Hardy inequality on the integers. We prove the optimality of the Hardy weight and hence affirmatively answer the question of sharpness of the constant.
math.AP2022
Gaussian upper bounds for heat kernels on graphs with unbounded geometry
Matthias Keller, Christian Rose
We prove large-time Gaussian upper bounds for continuous-time heat kernels of Laplacians on graphs with unbounded geometry. Our estimates hold for centers of large balls satisfying…