The support of a function with thin spectrum
Hare, Kathryn
Colloquium Mathematicae, Tome 67 (1994), p. 147-154 / Harvested from The Polish Digital Mathematics Library
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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 ∥f1S∥2≥c∥f∥2 for all f∈L2(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.

Publié le : 1994-01-01
EUDML-ID : urn:eudml:doc:210257 
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Hare, Kathryn. The support of a function with thin spectrum. Colloquium Mathematicae, Tome 67 (1994) pp. 147-154. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv67i1p147bwm/

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