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.
On pattern entropy of weak model sets
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abstract
We study point sets arising from cut-and-project constructions. An important class is weak model sets, which include squarefree numbers and visible lattice points. For such model sets, we give a non-trivial upper bound on their pattern entropy in terms of the volume of the window boundary in internal space. This proves a conjecture by R.V. Moody.
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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.