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Average sampling and reconstruction in a reproducing kernel subspace of homogeneous type space

In this paper, we first introduce a reproducing kernel subspace of Lp(X,ρ,μ) , where (X,ρ,μ) is a homogeneous type space. Then we consider average sampling and reconstruction of signals in the reproducing kernel subspace of Lp(X,ρ,μ),1≤p≤∞ . We show that signals in the reproducing kernel subspace of Lp(X,ρ,μ) could be stably reconstructed from its average samples taken on a relatively‐separated set with small gap. Exponential convergence is established for the iterative approximation‐projection reconstruction algorithm.