Convolutional dynamical sampling and some new results
<|reference_start|>Convolutional dynamical sampling and some new results: In this work, we explore the dynamical sampling problem on $\ell^2(\mathbb{Z})$ driven by a convolution operator defined by a convolution kernel. This problem is inspired by the need to recover a bandlimited heat diffusion field from space-time samples and its discrete analogue. In this book chapter, we review recent results in the finite-dimensional case and extend these findings to the infinite-dimensional case, focusing on the study of the density of space-time sampling sets.<|reference_end|>
@article{huang2024convolutional,
    title={Convolutional dynamical sampling and some new results},
    author={Longxiu Huang, A. Martina Neuman, Sui Tang, and Yuying Xie},
    journal={arXiv preprint arXiv:2406.15122},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.15122},
    primaryClass={cs.IT math.IT}
}