Abstract
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.
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Communicated by Hans G. Feichtinger.
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Runovski, K., Schmeisser, HJ. On Approximation Methods Generated by Bochner-Riesz Kernels. J Fourier Anal Appl 14, 16–38 (2008). https://doi.org/10.1007/s00041-007-9004-y
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DOI: https://doi.org/10.1007/s00041-007-9004-y
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