Geodesic
The support of a function with thin spectrum
Colloquium Mathematicum, Tome 67 (1994) no. 1, pp. 147-154

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We prove that if $E ⊆ Ĝ$ does not contain parallelepipeds of arbitrarily large dimension then for any open, non-empty $S ⊆ G$ there exists a constant c > 0 such that $∥ f1_S ∥_2 ≥ c ∥ f ∥ _2$ for all $f ∈ L^2(G)$ whose Fourier transform is supported on E. In particular, such functions cannot vanish on any open, non-empty subset of G. Examples of sets which do not contain parallelepipeds of arbitrarily large dimension include all Λ(p) sets.
DOI : 10.4064/cm-67-1-147-154

Kathryn Hare 1

1 
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Kathryn Hare. The support of a function with thin spectrum. Colloquium Mathematicum, Tome 67 (1994) no. 1, pp. 147-154. doi: 10.4064/cm-67-1-147-154

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