Crystalline temperate distributions with uniformly discrete support and spectrum

Crystalline temperate distributions with uniformly discrete support and spectrum

We prove that a temperate distribution on R whose support and spectrum are uniformly discrete sets, can be obtained from Poisson's summation formula by a finite number of basic operations (shifts, modulations, differentiations, multiplication by polynomials, and taking linear combinations).

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Veröffentlicht in:Journal of functional analysis 2021-08, Vol.281 (4), p.109072, Article 109072
Hauptverfasser: Lev, Nir, Reti, Gilad
Format: Artikel
Sprache:eng
Schlagworte:
Poisson's summation formula
Quasicrystals
Temperate distributions
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Zusammenfassung:We prove that a temperate distribution on R whose support and spectrum are uniformly discrete sets, can be obtained from Poisson's summation formula by a finite number of basic operations (shifts, modulations, differentiations, multiplication by polynomials, and taking linear combinations).
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2021.109072