2024/09/13 by Meng Ning, Ning, Meng, Liping Wu +5
Mathematics · #42C15 #94A12 #94A20 #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2409.08506
openalex publication_date 2024/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Special Affine Fourier Transformation(SAFT), which generalizes several well-known unitary transformations, has been demonstrated as a valuable tool in signal processing and optics. In this paper, we explore the multivariate dynamical sampling problem in shift-invariant spaces associated with the multi-dimensional SAFT. Specifically, we derive a sufficient and necessary condition under which a function in a shift-invariant space can be stably recovered from its dynamical sampling measurements associated with the multi-dimensional SAFT . We also present a straightforward example to elucidate our main result.