Leptin Densities in Amenable Groups

Pogorzelski F, Richard C, Strungaru N (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Journal of Fourier Analysis and Applications Springer Verlag (Germany)

Book Volume: 28

Journal Issue: 6

DOI: 10.1007/s00041-022-09978-8

Abstract

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 1966. We then restrict to unimodular amenable groups and to translation bounded measures. In that case our density notion coincides with the well-known Beurling density from Fourier analysis, also known as Banach density from dynamical systems theory. We use Leptin densities for a geometric proof of the model set density formula, which expresses the density of a uniform regular model set in terms of the volume of its window, and for a proof of uniform mean almost periodicity of such model sets.

Authors with CRIS profile

Christoph Richard Lehrstuhl für Mathematische Stochastik

Involved external institutions

Universität Leipzig DE Germany (DE) MacEwan University CA Canada (CA)

How to cite

APA:

Pogorzelski, F., Richard, C., & Strungaru, N. (2022). Leptin Densities in Amenable Groups. Journal of Fourier Analysis and Applications, 28(6). https://dx.doi.org/10.1007/s00041-022-09978-8

MLA:

Pogorzelski, Felix, Christoph Richard, and Nicolae Strungaru. "Leptin Densities in Amenable Groups." Journal of Fourier Analysis and Applications 28.6 (2022).

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