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- W2996282904 abstract "In the framework of a strictly local regular Dirichlet space X we introduce the subspaces PWω, ω > 0, of Paley–Wiener functions of bandwidth ω. It is shown that every function in PWω, ω > 0, is uniquely determined by its average values over a family of balls B(xj, ρ), xj ∈X, which form an admissible cover of X and whose radii are comparable to ω−1∕2. The entire development heavily depends on some Poincare-type inequalities. In the second part of the paper we realize the same idea in the setting of a weighted combinatorial finite or infinite graph G. We have to treat the case of graphs separately since the Poincare inequalities we are using on them are somewhat different from the Poincare inequalities in the first part." @default.
- W2996282904 created "2019-12-26" @default.
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- W2996282904 date "2021-01-01" @default.
- W2996282904 modified "2023-09-26" @default.
- W2996282904 title "Sampling by Averages and Average Splines on Dirichlet Spaces and on Combinatorial Graphs" @default.
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- W2996282904 doi "https://doi.org/10.1007/978-3-030-69637-5_14" @default.
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