4 papers
Eigenvalue growth of the discrete Hodge Laplacian across dimensions
Philipp Bartmann, Matthias Keller
We prove several bounds on the largest and smallest eigenvalues of the combinatorial Hodge Laplacian of a finite simplicial complex As a consequence, we obtain new van…
Coupling of the continuum and semiclassical limit. Part I: convergence of eigenvalues
Matthias Keller, Lorenzo Pettinari, Christiaan J. F. van de Ven
We analyze the semiclassical -dimensional Schrödinger operator in the continuum discretized on a mesh with spacing proportional to . The semi-c…
The heat equation and independence of the spectrum of the Hodge Laplacian on
Philipp Bartmann, Matthias Keller
We study the heat equation associated to the Hodge Laplacian on simplicial complexes. Using recently developed techniques for magnetic Schrödinger operators, we prove Davies-Gaffn…
Optimal Hardy Inequality for Fractional Laplacians on the Lattice
Philipp Hake, Matthias Keller, Felix Pogorzelski
We study the fractional Hardy inequality on the integer lattice. We prove null-criticality of the Hardy weight and hence optimality of the constant. More specifically, we present a…