Some new thin sets of integers in harmonic analysis |
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Authors: | D Li H Queffélec L Rodríguez-Piazza |
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Institution: | 1. P?le de Lens Faculté des Sciences Jean Perrin, Université d’Artois, rue Jean Souvraz SP 18, F-62307, Lens Cedex, France 2. UFR de Mathématiques, Université des Sciences et Technologies de Lille, F-59655, Villeneuve d’Ascq Cedex, France 3. Facultad de Matematicas Departamento de Análisis Matemático, Universidad de Sevilla, Apartado de Correos 1160, 41080, Sevilla, Spain
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Abstract: | We randomly construct various subsets A of the integers which have both smallness and largeness properties. They are small
since they are very close, in various senses, to Sidon sets: the continuous functions with spectrum in Λ have uniformly convergent
series, and their Fourier coefficients are in ℓp for all p > 1; moreover, all the Lebesgue spaces L
Λ
q
are equal forq < +∞. On the other hand, they are large in the sense that they are dense in the Bohr group and that the space of the bounded
functions with spectrum in Λ is nonseparable. So these sets are very different from the thin sets of integers previously known. |
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Keywords: | |
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