Please use this identifier to cite or link to this item: https://doi.org/10.1007/s00041-005-4003-3
Title: Convolution, average sampling, and a calderon resolution of the identity for shift-invariant spaces
Authors: Aldroubi, A.
Sun, Q.
Tang, W.-S. 
Issue Date: Apr-2005
Citation: Aldroubi, A., Sun, Q., Tang, W.-S. (2005-04). Convolution, average sampling, and a calderon resolution of the identity for shift-invariant spaces. Journal of Fourier Analysis and Applications 11 (2) : 215-244. ScholarBank@NUS Repository. https://doi.org/10.1007/s00041-005-4003-3
Abstract: In this article, we study three interconnected inverse problems in shift invariant spaces: 1) the convolution/deconvolution problem; 2) the uniformly sampled convolution and the reconstruction problem; 3) the sampled convolution followed by sampling on irregular grid and the reconstruction problem. In all three cases, we study both the stable reconstruction as well as ill-posed reconstruction problems. We characterize the convolutors for stable deconvolution as well as those giving rise to ill-posed deconvolution. We also characterize the convolutors that allow stable reconstruction as well as those giving rise to ill-posed reconstruction from uniform sampling. The connection between stable deconvolution, and stable reconstruction from samples after convolution is subtle, as will be demonstrated by several examples and theorems that relate the two problems. © 2005 Birkhäuser Boston. All rights reserved.
Source Title: Journal of Fourier Analysis and Applications
URI: http://scholarbank.nus.edu.sg/handle/10635/103077
ISSN: 10695869
DOI: 10.1007/s00041-005-4003-3
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