Year: 2024
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Huang, Longxiu, Neuman, A. Martina, Tang, Sui, Xie, Yuying
Institution: Michigan State University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: Data-Driven Discovery of Dynamics in Interacting Agent Systems and Linear Diffusion Processes, Collaborative Research: HDR DSC: Increasing Accessibility through Building Alternative Data Science Pathways, CAREER: Solving Estimation Problems of Networked Interacting Dynamical Systems Via Exploiting Low Dimensional Structures: Mathematical Foundations, Algorithms and Applications, TRTech-PGR: Connecting sequences to functions within and between species through computational modeling and experimental studies, G9000113691, G9000117357
OpenAlex ID: W4399991086