Submodules of $H^2(\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908441554976768 |
|---|---|
| author | Bailey, Victor Cabrelli, Carlos |
| author_facet | Bailey, Victor Cabrelli, Carlos |
| contents | Recent work in Dynamical Sampling has been centered on characterizing frames obtained by the orbit of a vector under a bounded operator. We prove a necessary and sufficient condition for a pair of bounded commuting operators on a separable infinite-dimensional Hilbert space to generate a frame by unilateral iterations on a single vector. Applying the theory on submodules of the Hardy module $H^2(\mathbb{T}^2)$, we characterize these frames in terms of their relation to the two-variable Jordan block on a certain quotient module and provide some properties of frames of this form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04992 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Submodules of $H^2(\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators Bailey, Victor Cabrelli, Carlos Functional Analysis 46C99, 47A99 Recent work in Dynamical Sampling has been centered on characterizing frames obtained by the orbit of a vector under a bounded operator. We prove a necessary and sufficient condition for a pair of bounded commuting operators on a separable infinite-dimensional Hilbert space to generate a frame by unilateral iterations on a single vector. Applying the theory on submodules of the Hardy module $H^2(\mathbb{T}^2)$, we characterize these frames in terms of their relation to the two-variable Jordan block on a certain quotient module and provide some properties of frames of this form. |
| title | Submodules of $H^2(\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators |
| topic | Functional Analysis 46C99, 47A99 |
| url | https://arxiv.org/abs/2507.04992 |