Irregular sampling for hyperbolic secant type functions
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911777343668224 |
|---|---|
| author | Baranov, Anton Belov, Yurii |
| author_facet | Baranov, Anton Belov, Yurii |
| contents | We study Gabor frames in the case when the window function is of hyperbolic secant type, i.e., $g(x) = (e^{ax}+e^{-bx})^{-1}$, ${\rm Re}\,a, {\rm Re}\,b>0$. A criterion for half-irregular sampling is obtained: for a separated $Λ\subset\mathbb{R}$ the Gabor system $\mathcal{G}(g, Λ\times α\Z)$ is a frame in $L^2(\R)$ if and only if $D^-(Λ) >α$ where $D^-(Λ)$ is the usual (Beurling) lower density of $Λ$. This extends a result by Gröchenig, Romero, and Stöckler which applies to the case of a standard hyperbolic secant. Also, a full description of complete interpolating sequences for the shift-invariant space generated by $g$ is given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10174 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Irregular sampling for hyperbolic secant type functions Baranov, Anton Belov, Yurii Functional Analysis Complex Variables Primary 30H20, Secondary 30D10, 30E05, 42C15, 94A20 We study Gabor frames in the case when the window function is of hyperbolic secant type, i.e., $g(x) = (e^{ax}+e^{-bx})^{-1}$, ${\rm Re}\,a, {\rm Re}\,b>0$. A criterion for half-irregular sampling is obtained: for a separated $Λ\subset\mathbb{R}$ the Gabor system $\mathcal{G}(g, Λ\times α\Z)$ is a frame in $L^2(\R)$ if and only if $D^-(Λ) >α$ where $D^-(Λ)$ is the usual (Beurling) lower density of $Λ$. This extends a result by Gröchenig, Romero, and Stöckler which applies to the case of a standard hyperbolic secant. Also, a full description of complete interpolating sequences for the shift-invariant space generated by $g$ is given. |
| title | Irregular sampling for hyperbolic secant type functions |
| topic | Functional Analysis Complex Variables Primary 30H20, Secondary 30D10, 30E05, 42C15, 94A20 |
| url | https://arxiv.org/abs/2312.10174 |