The support of a function with thin spectrum

Kathryn Hare

Colloquium Mathematicae (1994)

  • Volume: 67, Issue: 1, page 147-154
  • ISSN: 0010-1354

Abstract

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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 ∥ f 1 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.

How to cite

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Hare, Kathryn. "The support of a function with thin spectrum." Colloquium Mathematicae 67.1 (1994): 147-154. <http://eudml.org/doc/210257>.

@article{Hare1994,
abstract = {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.},
author = {Hare, Kathryn},
journal = {Colloquium Mathematicae},
keywords = {subtransversal; associatedness; parallelepipeds},
language = {eng},
number = {1},
pages = {147-154},
title = {The support of a function with thin spectrum},
url = {http://eudml.org/doc/210257},
volume = {67},
year = {1994},
}

TY - JOUR
AU - Hare, Kathryn
TI - The support of a function with thin spectrum
JO - Colloquium Mathematicae
PY - 1994
VL - 67
IS - 1
SP - 147
EP - 154
AB - 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.
LA - eng
KW - subtransversal; associatedness; parallelepipeds
UR - http://eudml.org/doc/210257
ER -

References

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  10. [10] S. Mandelbrojt, Séries de Fourier et classes quasi-analytiques de fonctions, Gauthier-Villars, Paris, 1935. Zbl0013.11006
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