Sampling theory with average values on the Sierpinski gasket (Q329459)

The authors consider the analogs of classical sampling theorems for self-similar subsets of \(\mathbb{R}^2\), i.e., for subsets that are a finite union of their images under contractive similitudes. Their investigation focuses entirely on the Sierpiński gasket \(SG\) and a related object, \(SG_3\). In particular, it is shown that the cell graph approximations possess the spectral decomposition property and thus the analog of the Shannon sampling theorem is proven for \(SG\). In contrast, although \(SG_3\) also has the spectral decomposition property, it does not help to prove a sampling theorem.