Periodic Source Detection in Discrete Dynamical Systems via space-time sampling
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909286250053632 |
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| author | Aldroubi, Akram Cabrelli, Carlos Molter, Ursula |
| author_facet | Aldroubi, Akram Cabrelli, Carlos Molter, Ursula |
| contents | In this paper, we examine a discrete dynamical system defined by x(n+1) = Ax(n)+ w(n), where x takes values in a Hilbert space H and w is a periodic source with values in a fixed closed subspace W of H. Our goal is to identify conditions on some spatial sampling system G = {gj: j in J} of H that enable stable recovery of the unknown source term w from space-time samples {<x(n),g_j>: n >=0,j in J}. We provide necessary and sufficient conditions on G = {g_j }_{j in J} to ensure stable recovery of any w in W . Additionally, we explicitly construct an operator R, dependent on G, such that R{<x(n),g_j>}_n,j} = w. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_06934 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Periodic Source Detection in Discrete Dynamical Systems via space-time sampling Aldroubi, Akram Cabrelli, Carlos Molter, Ursula Classical Analysis and ODEs 41A65, 43A70 In this paper, we examine a discrete dynamical system defined by x(n+1) = Ax(n)+ w(n), where x takes values in a Hilbert space H and w is a periodic source with values in a fixed closed subspace W of H. Our goal is to identify conditions on some spatial sampling system G = {gj: j in J} of H that enable stable recovery of the unknown source term w from space-time samples {<x(n),g_j>: n >=0,j in J}. We provide necessary and sufficient conditions on G = {g_j }_{j in J} to ensure stable recovery of any w in W . Additionally, we explicitly construct an operator R, dependent on G, such that R{<x(n),g_j>}_n,j} = w. |
| title | Periodic Source Detection in Discrete Dynamical Systems via space-time sampling |
| topic | Classical Analysis and ODEs 41A65, 43A70 |
| url | https://arxiv.org/abs/2408.06934 |