Spans of translates in weighted ℓ p spaces

• Karim Kellay ^[1] ; Florian Le Manach ^[1] ; Mohamed Zarrabi ^[1]
  1. [1] University of Bordeaux

     University of Bordeaux

     Arrondissement de Bordeaux, Francia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 39, Nº 5, 2023, págs. 1925-1946
• Idioma: inglés
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• Resumen

  • We study the cyclic vectors and the spanning set of the circle for the ` p ˇ .Z/ spaces of all sequences u D .un/n2Z such that .un.1 C jnj/ ˇ /n2Z 2 ` p.Z/, with p > 1 and ˇ > 0. The uniqueness set of the distribution on the circle whose Fourier coefficients are in ` q ˇ .Z/ is the spanning set for the ` p ˇ .Z/spaces, where q is the conjugate of p. Our characterizations are given in terms of the Hausdorff dimension and capacity