Aperiodic order and spherical diffraction, III: The shadow transform and the diffraction formula
Artikel i vetenskaplig tidskrift, 2021

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 the hyperbolic plane we can interpret the spherical diffraction measure as the Mellin transform of the auto-correlation distribution. We show that uniform regular model sets in commutative spaces have a pure point spherical diffraction measure. The atoms of this measure are located at the spherical automorphic spectrum of the underlying lattice, and the diffraction coefficients can be characterized abstractly in terms of the so-called shadow transform of the characteristic functions of the window. In the case of the Heisenberg group we can give explicit formulas for these diffraction coefficients in terms of Bessel and Laguerre functions. (C) 2021 The Author(s). Published by Elsevier Inc.

Aperiodic order

Spherical diffraction

Gelfand pair


Michael Björklund

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Tobias Hartnick

Karlsruher Institut für Technologie (KIT)

Felix Pogorzelski

Universität Leipzig

Journal of Functional Analysis

0022-1236 (ISSN) 1096-0783 (eISSN)

Vol. 281 12 109265


Algebra och logik


Matematisk analys



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