Resumen de Spans of translates in weighted ℓ p spaces

Karim Kellay, Florian Lehner, Mohamed Zarrabi

• 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