Dynamical Sampling: A Survey
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917392125263872 |
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| author | Aldroubi, Akram Cabrelli, Carlos Krishtal, Ilya Molter, Ursula |
| author_facet | Aldroubi, Akram Cabrelli, Carlos Krishtal, Ilya Molter, Ursula |
| contents | Dynamical sampling refers to a class of problems in which space-time samples are taken from a signal evolving under an underlying dynamical system. The goal is to use these samples to recover relevant information about the system, such as the initial state, the evolution operator, or the sources and sinks driving the dynamics. These problems are tightly connected to frame theory, operator theory, functional analysis, and other foundational areas of mathematics; they also give rise to new theoretical questions and have applications across engineering and the sciences. This survey provides an overview of the theoretical underpinnings of dynamical sampling, summarizes recent results, and outlines directions for future work, including open problems and conjectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10769 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamical Sampling: A Survey Aldroubi, Akram Cabrelli, Carlos Krishtal, Ilya Molter, Ursula Functional Analysis Dynamical Systems Operator Algebras Optimization and Control Spectral Theory 42C15, 47A10, 94A20, 65T60, 93B30, 93C05 Dynamical sampling refers to a class of problems in which space-time samples are taken from a signal evolving under an underlying dynamical system. The goal is to use these samples to recover relevant information about the system, such as the initial state, the evolution operator, or the sources and sinks driving the dynamics. These problems are tightly connected to frame theory, operator theory, functional analysis, and other foundational areas of mathematics; they also give rise to new theoretical questions and have applications across engineering and the sciences. This survey provides an overview of the theoretical underpinnings of dynamical sampling, summarizes recent results, and outlines directions for future work, including open problems and conjectures. |
| title | Dynamical Sampling: A Survey |
| topic | Functional Analysis Dynamical Systems Operator Algebras Optimization and Control Spectral Theory 42C15, 47A10, 94A20, 65T60, 93B30, 93C05 |
| url | https://arxiv.org/abs/2511.10769 |