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Means and families of operators generated by Bochner-Riesz kernels are studied. Some sharp results on their convergence are achieved. The equivalence of the approximation errors of these methods to smoothness quantities related to the Laplacian is proved.Keywords Bochner-Riesz kernels and means · Families of operators · Necessary and sufficient conditions of convergence · K-functional · Realizations and moduli of smoothness related to the Laplacian Mathematics Subject Classification (2000) 42A10 · 42A15

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