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Generalised Sampling Approximation Theorems

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Approximation properties of different generalizations of multivariate sampling expansions with matrix dilation are studied. Error estimations for so-called ’’differential expansions’’ and ’’falsified expansions’’ are given in terms of the Fourier transform of the approximated function. Another special case is generalized Kantorovich-Kotelnikov expansions. For this case, the rate of convergence is given in terms of the classical moduli of smoothness of the approximated function. Several examples of the Kantorovich-Kotelnikov operators generated by the sink-function and its linear combinations are provided.

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