On planar sampling with Gaussian kernel in spaces of bandlimited functions
| Autor: | Zlotnikov, Ilya |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | J Fourier Anal Appl 28, 55 (2022) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00041-022-09948-0 |
| Popis: | Let $I=(a,b)\times(c,d)\subset {\mathbb R}_{+}^2$ be an index set and let $\{G_{\alpha}(x) \}_{\alpha \in I}$ be a collection of Gaussian functions, i.e. $G_{\alpha}(x) = \exp(-\alpha_1 x_1^2 - \alpha_2 x_2^2)$, where $\alpha = (\alpha_1, \alpha_2) \in I, \, x = (x_1, x_2) \in {\mathbb R}^2$. We present a complete description of the uniformly discrete sets $\Lambda \subset {\mathbb R}^2$ such that every bandlimited signal $f$ admits a stable reconstruction from the samples $\{f \ast G_{\alpha} (\lambda)\}_{\lambda \in \Lambda}$. Comment: 22 pages, 1 figure |
| Databáze: | arXiv |
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