Doubly sparse measures on second countable locally compact Abelian groups are shown to be supported on finitely many translates of a lattice with trigonometric polynomial amplitudes.
Model sets: a survey
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abstract
This article surveys the mathematics of the cut and project method as applied to point sets, called here {\em model sets}. It covers the geometric, arithmetic, and analytical sides of this theory as well as diffraction and the connection with dynamical systems.
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math.MG 1years
2019 1verdicts
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Pure point measures with sparse support and sparse Fourier--Bohr support
Doubly sparse measures on second countable locally compact Abelian groups are shown to be supported on finitely many translates of a lattice with trigonometric polynomial amplitudes.