## Abstract

The purpose of this paper is to establish L^{p} error estimates, a Bernstein inequality, and inverse theorems for approximation by a space comprising spherical basis functions located at scattered sites on the unit n-sphere. In particular, the Bernstein inequality estimates L^{p} Bessel-potential Sobolev norms of functions in this space in terms of the minimal separation and the L^{p} norm of the function itself. An important step in its proof involves measuring the L^{p} stability of functions in the approximating space in terms of the £^{p} norm of the coefficients involved. As an application of the Bernstein inequality, we derive inverse theorems for SBF approximation in the L^{p} norm. Finally, we give a new characterization of Besov spaces on the n-sphere in terms of spaces of SBFs.

Original language | English |
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Journal | Mathematics of Computation |

Volume | 79 |

Issue number | 271 |

Pages (from-to) | 1647-1679 |

Number of pages | 33 |

ISSN | 0025-5718 |

DOIs | |

Publication status | Published - 01.07.2010 |

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