TY - JOUR
T1 - No characterization of generators in ℓp(1 < p < 2) by zero set of Fourier transform
AU - Lev, Nir
AU - Olevskii, Alexander
PY - 2008/6
Y1 - 2008/6
N2 - Given 1 < p < 2 we construct two continuous functions f and g on the circle, with the following properties:. (i) They have the same set of zeros;. (ii) The Fourier transforms over(f, ̂) and over(g, ̂) both belong to ℓp (Z);. (iii) The translates of over(g, ̂) span the whole ℓp, but those of over(f, ̂) do not. A similar result is true for Lp (R). This should be contrasted with the Wiener theorems related to p = 1, 2. To cite this article: N. Lev, A. Olevskii, C. R. Acad. Sci. Paris, Ser. I 346 (2008).
AB - Given 1 < p < 2 we construct two continuous functions f and g on the circle, with the following properties:. (i) They have the same set of zeros;. (ii) The Fourier transforms over(f, ̂) and over(g, ̂) both belong to ℓp (Z);. (iii) The translates of over(g, ̂) span the whole ℓp, but those of over(f, ̂) do not. A similar result is true for Lp (R). This should be contrasted with the Wiener theorems related to p = 1, 2. To cite this article: N. Lev, A. Olevskii, C. R. Acad. Sci. Paris, Ser. I 346 (2008).
UR - http://www.scopus.com/inward/record.url?scp=44449112607&partnerID=8YFLogxK
U2 - 10.1016/j.crma.2008.04.017
DO - 10.1016/j.crma.2008.04.017
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SN - 1631-073X
VL - 346
SP - 645
EP - 648
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 11-12
ER -