The support of a function with thin spectrum

• Autorzy: Kathryn E. Hare
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1994
• Tom: 67
• Numer: 1
• Strony: 147-154

Daty

wydano

1994

otrzymano

1993-02-01

poprawiono

1993-12-14

Twórcy

autor

Kathryn E. Hare

• Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

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