Convolution sampling and reconstruction of signals in a reproducing kernel subspace (Q2838957)

Sampling expansions in reproducing kernel Hilbert and Banach spaces were investigated in [\textit{D. Han} et al., Numer. Funct. Anal. Optim. 30, No. 9--10, 971--987 (2009; Zbl 1183.42032)]. In the paper under review the stability of the convolution sampling for signals in the reproducing kernel subspace \(V_{p}\) of \(L^{p}(\mathbb{R}^{d})\), \(1\leq p<\infty\), is investigated. In other words, the authors show that each signal in \(V_{p}\) can be stably reconstructed from its convolution samples taken on a sample set having sufficiently small gap. They also state exponential convergence and error estimates of the iterative approximation-projection algorithm to reconstructed signals in \(V_{p}\).