Spectral theory of approximate lattices in nilpotent Lie groups
Artikel i vetenskaplig tidskrift, 2021

We consider approximate lattices in nilpotent Lie groups. With every such approximate lattice one can associate a hull dynamical system and, to every invariant measure of this system, a corresponding unitary representation. Our results concern both the spectral theory of the representation and the topological dynamics of the system. On the spectral side we construct explicit eigenfunctions for a large collection of central characters using weighted periodization against a twisted fiber density function. We construct this density function by establishing a parametric version of the Bombieri-Taylor conjecture and apply our results to locate high-intensity Bragg peaks in the central diffraction of an approximate lattice. On the topological side we show that under some mild regularity conditions the hull of an approximate lattice admits a sequence of continuous horizontal factors, where the final horizontal factor is abelian and each intermediate factor corresponds to a central extension. We apply this to extend theorems of Meyer and Dani-Navada concerning number-theoretic properties of Meyer sets to the nilpotent setting.


Michael Björklund

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Tobias Hartnick

Karlsruher Institut für Technologie (KIT)

Mathematische Annalen

0025-5831 (ISSN) 1432-1807 (eISSN)

Vol. In Press


Algebra och logik


Matematisk analys



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