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Journal Articles Revista Matemática Iberoamericana Year : 2023

SPANS OF TRANSLATES IN WEIGHTED $\ell^p$ SPACES

Karim Kellay
Florian Le Manach
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Mohamed Zarrabi

Abstract

We study the cyclic vectors and the spanning set of the circle for the $\ell^p_\beta β(\mathbb{Z}$ spaces of all sequences $u =(u_ n)_{n\in \mathbb{Z}}$ such that $(u_n (1 + |n|)^\beta)_{ n\in \mathbb{Z}}\in \ell^p (\mathbb{Z}$ with $p > 1$ and $\beta>0$. By duality the spanning set is the uniqueness set of the distribution on the circle whose Fourier coefficients are in $\ell^{q}_{−\beta} (\mathbb{Z}$) where $q$ is the conjugate of $p$. Our characterizations are given in terms of the Hausdorff dimension and capacity.
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Dates and versions

hal-03790054 , version 1 (28-09-2022)

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  • HAL Id : hal-03790054 , version 1

Cite

Karim Kellay, Florian Le Manach, Mohamed Zarrabi. SPANS OF TRANSLATES IN WEIGHTED $\ell^p$ SPACES. Revista Matemática Iberoamericana, inPress. ⟨hal-03790054⟩

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