Periodic Source Detection in Discrete Dynamical Systems via space-time sampling
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.06934
- arXiv:
- arXiv:2408.06934
- Bibcode:
- 2024arXiv240806934A
- Keywords:
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- Mathematics - Classical Analysis and ODEs;
- 41A65;
- 43A70
- E-Print:
- 12 pages