3 citations · 11 across the 9 of their papers we have counts for
10 papers
Optimal Hardy Inequalities for Fractional -Laplacians on the Integers
Florian Fischer, Marius Nietschmann
We obtain optimal Hardy inequalities for fractional powers of the -Laplacian on , , . Asymptotically, the optimal weights beh…
Characterizations of -Parabolicity on Graphs
Andrea Adriani, Florian Fischer, Alberto G. Setti
We study -energy functionals on infinite locally summable graphs for and show that many well-known characterizations for a parabolic space are also true in thi…
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…
Capacity of infinite graphs over non-Archimedean ordered fields
Florian Fischer, Matthias Keller, Anna Muranova +1
In this article we study the notion of capacity of a vertex for infinite graphs over non-Archimedean fields. In contrast to graphs over the real field monotone limits do not need t…
Sharp Hardy-type inequalities for non-compact harmonic manifolds and Damek-Ricci spaces
Florian Fischer, Norbert Peyerimhoff
We show various sharp Hardy-type inequalities for the linear and quasi-linear Laplacian on non-compact harmonic manifolds with a particular focus on the case of Damek-Ricci spaces.…
On the Optimality and Decay of -Hardy Weights on Graphs
Florian Fischer
We construct optimal Hardy weights to subcritical energy functionals associated with quasilinear Schrödinger operators on locally finite graphs. Here, optimality means that the…
Quasi-Linear Criticality Theory and Green's Functions on Graphs
Florian Fischer
We study energy functionals associated with quasi-linear Schrödinger operators on infinite graphs, and develop characterisations of (sub-)criticality via Green's functions, harmoni…
A Non-Local Quasi-Linear Ground State Representation and Criticality Theory
Florian Fischer
We study energy functionals associated with non-local quasi-linear Schrödinger operators, and develop a ground state representation. Our main focus is on infinite graphs but we als…
An Improved Discrete -Hardy Inequality
Florian Fischer, Matthias Keller, Felix Pogorzelski
We improve the classical discrete Hardy inequality for for functions on the natural numbers. For integer values of the Hardy weight is an absolutely monotonic…
Riesz Decompositions for Schrödinger Operators on Graphs
Florian Fischer, Matthias Keller
We study superharmonic functions for Schrödinger operators on general weighted graphs. Specifically, we prove two decompositions which both go under the name Riesz decomposition in…