Pogorzelski F, Richard C, Strungaru N (2022)
Publication Type: Journal article
Publication year: 2022
Book Volume: 28
Journal Issue: 6
DOI: 10.1007/s00041-022-09978-8
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.
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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