4 papers
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…
Borel density for approximate lattices
Michael Björklund, Tobias Hartnick, Thierry Stulemeijer
We extend classical density theorems of Borel and Dani--Shalom on lattices in semisimple, respectively solvable algebraic groups over local fields to approximate lattices. Our proo…
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…
Central Limit Theorems for group actions which are exponentially mixing of all orders
Michael Björklund, Alexander Gorodnik
In this paper we establish a general dynamical Central Limit Theorem (CLT) for group actions which are exponentially mixing of all orders. In particular, the main result applies to…