SPANS OF TRANSLATES IN WEIGHTED $\ell^p$ SPACES
Language
en
Article de revue
This item was published in
Revista Matemática Iberoamericana. 2023-01-17
European Mathematical Society
Date
2023-01-17English 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 ...Read more >
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.Read less <
English Keywords
2000 Mathematics Subject Classification. primary 43A15
secondary 28A12
42A38 Cyclicity
Weighted p spaces
Spanning set
Uniqueness set
Hausdorff dimension
Capacity
Origin
Hal imported