27 citations · 116 across the 31 of their papers we have counts for
9 papers · 1 filter
Siegel-Radon transforms of transverse dynamical systems
Michael Björklund, Tobias Hartnick
We extend Helgason's classical definition of a generalized Radon transform, defined for a pair of homogeneous spaces of an lcsc group , to a broader setting in which one of the…
Dynamics on spaces of quasimorphisms and applications to approximate lattice theory
Michael Björklund, Tobias Hartnick
We study the dynamics of countable groups on their respective spaces of quasimorphisms. For cohomologically non-trivial quasimorphisms we show that there are no invariant measures…
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…
Intersection spaces and multiple transverse recurrence
Michael Björklund, Tobias Hartnick, Yakov Karasik
We study multiple recurrence properties along separated cross sections for pmp actions of unimodular lcsc group on Polish spaces. We establish a multiple transverse recurrence theo…
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…
Spectral theory of approximate lattices in nilpotent Lie groups
Michael Björklund, Tobias Hartnick
We show that an approximate lattice in a nilpotent Lie group admits a relatively dense subset of central -Bragg peaks for every . For the Heisenberg group we deduce th…
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…
Aperiodic order and spherical diffraction, I: Auto-correlation of model sets
Michael Björklund, Tobias Hartnick, Felix Pogorzelski
We study uniform and non-uniform model sets in arbitrary locally compact second countable (lcsc) groups, which provide a natural generalization of uniform model sets in locally com…