L^p Bernstein estimates and approximation by spherical basis functions

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dc.creatorMhaskar, H. N.
dc.creatorNarcowich, F. J.
dc.creatorPrestin, J.
dc.creatorWard, J. D.
dc.date2008-10-28
dc.date.accessioned2026-07-07T10:13:40Z
dc.date.available2026-07-07T10:13:40Z
dc.descriptionThe 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 l^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.
dc.identifierhttps://arxiv.org/abs/0810.5075
dc.identifierhttp://arxiv.org/abs/0810.5075
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172612
dc.subjectFunctional Analysis
dc.subjectClassical Analysis and ODEs
dc.subject41A17, 41A27, 41A63, 42C15
dc.titleL^p Bernstein estimates and approximation by spherical basis functions
dc.typetext

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