23 citations · 65 across the 22 of their papers we have counts for
34 papers
Optimal Hardy Inequalities for Random Walks on
Philipp Hake, Matthias Keller, Felix Pogorzelski
We prove an optimal Hardy inequality for every aperiodic, symmetric random walk in with finite variance. In particular, we verify null-criticality, and thus, optimal…
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…
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 iteratin…
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…
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…
Mixing and equipartition for automorphism invariant processes on regular trees
Felix Pogorzelski, Elias Zimmermann
The paper is devoted to equipartition of measured information for finite state processes over regular trees whose laws are invariant under all parity preserving tree automorphisms.…
Spectral approximation for substitution systems
Ram Band, Siegfried Beckus, Felix Pogorzelski +1
We study periodic approximations of aperiodic Schrödinger operators on lattices in Lie groups with dilation structure. The potentials arise through symbolic substitution systems th…
Shannon-McMillan-Breiman theorem along almost geodesics in negatively curved groups
Amos Nevo, Felix Pogorzelski
Consider a non-elementary Gromov-hyperbolic group with a suitable invariant hyperbolic metric, and an ergodic probability measure preserving (p.m.p.) action on . We cons…
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…
Symbolic substitution systems beyond abelian groups
Siegfried Beckus, Tobias Hartnick, Felix Pogorzelski
In this article we construct the first examples of strongly aperiodic linearly repetitive Delone sets in non-abelian Lie groups by means of symbolic substitutions. In particular, w…
Leptin densities in amenable groups
Felix Pogorzelski, Christoph Richard, Nicolae Strungaru
Consider a positive Borel measure on a locally compact group. We define a notion of uniform density for such a measure, which is based on a group invariant introduced by Leptin in…
Agmon estimates for Schrödinger operators on graphs
Matthias Keller, Felix Pogorzelski
We prove decay estimates for generalized eigenfunctions of discrete Schrödinger operators on weighted infinite graphs in the spirit of Agmon.
Aperiodic order and spherical diffraction, III: The shadow transform and the diffraction formula
Michael Björklund, Tobias Hartnick, Felix Pogorzelski
We define spherical diffraction measures for a wide class of weighted point sets in commutative spaces, i.e. proper homogeneous spaces associated with Gelfand pairs. In the case of…
Linear repetitivity beyond abelian groups
Siegfried Beckus, Tobias Hartnick, Felix Pogorzelski
We show that linearly repetitive weighted Delone sets in groups of polynomial growth have a uniquely ergodic hull. This result applies in particular to the linearly repetitive weig…
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…
From Hardy to Rellich inequalities on graphs
Matthias Keller, Yehuda Pinchover, Felix Pogorzelski
We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Lapla…
Delone dynamical systems and spectral convergence
Siegfried Beckus, Felix Pogorzelski
In the realm of Delone sets in locally compact, second countable, Hausdorff groups, we develop a dynamical systems approach in order to study the continuity behavior of measured qu…
Criticality theory for Schrödinger operators on graphs
Matthias Keller, Yehuda Pinchover, Felix Pogorzelski
We study Schrödinger operators given by positive quadratic forms on infinite graphs. From there, we develop a criticality theory for Schrödinger operators on general weighted graph…
Aperiodic order and spherical diffraction, II: Translation bounded measures on homogeneous spaces
Michael Björklund, Tobias Hartnick, Felix Pogorzelski
We study the auto-correlation measures of invariant random point processes in the hyperbolic plane which arise from various classes of aperiodic Delone sets. More generally, we stu…
The Shannon-McMillan-Breiman theorem beyond amenable groups
Amos Nevo, Felix Pogorzelski
We introduce a new isomorphism-invariant notion of entropy for measure preserving actions of arbitrary countable groups on probability spaces, which we call orbital Rokhlin entropy…
An improved discrete Hardy inequality
Matthias Keller, Yehuda Pinchover, Felix Pogorzelski
We improve the classical discrete Hardy inequality \begin{equation*}\label{1} \sum _{n=1}^{\infty }a_{n}^{2}\geq \left({\frac {1}{2}}\right)^{2} \sum _{n=1}^{\infty }\left({\frac {…
Optimal Hardy inequalities for Schrödinger operators on graphs
Matthias Keller, Yehuda Pinchover, Felix Pogorzelski
For a given subcritical discrete Schrödinger operator on a weighted infinite graph , we construct a Hardy-weight which is optimal in the following sense. The operator $H…