10 papers
Supersolution Construction and Optimal Hardy Inequality for Fractional Laplacians
Philipp Hake, Matthias Keller, Felix Pogorzelski
We give a new criterion to show optimality of Hardy weights for general operators on graphs via the supersolution construction. For Laplacians on graphs without killing terms this…
A Liouville Theorem for Domains in Graphs
Philipp Hake, Matthias Keller, Felix Pogorzelski +1
We show a Liouville theorem for domains in graphs with Dirichlet boundary conditions. More specifically, we characterize the non-existence of non-zero bounded harmonic functions. S…
Strict irreducibility of Markov chains and ergodicity of skew products
Pablo Lummerzheim, Felix Pogorzelski, Elias Zimmermann
We consider a family of measure preserving transformations, which act on a common probability space and are chosen at random by a stationary ergodic Markov chain. This setting defi…
Positive Criticality and Optimal Hardy Inequality for Fractional Laplacians
Philipp Hake, Matthias Keller, Felix Pogorzelski
We characterize positive critical Hardy weights for general Laplacians on weighted graphs. We then apply this result to fractional Laplacians on general graphs and use the characte…
Spectral pollution in substitution systems
Ram Band, Siegfried Beckus, Felix Pogorzelski +1
We study spectral properties of Schrödinger operators associated with substitution dynamical systems in higher dimensions. Focusing on periodic approximations generated by iterati…
Random operators, spectral measures, and local empirical convergence in sofic groups
Miguel Donoso-Echenique, Felix Pogorzelski, Michael Schrödl-Baumann
In this paper, we consider the problem of approximating the spectral distribution for a class of random operators over sofic groups. For this purpose, we make use of the concept of…