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Widths and optimal sampling in spaces of analytic functions

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Abstract

Let Ω be a finitely-connected planar domain and μ be a positive measure with compact supportE in Ω. LetA p be the unit ball of the Hardy spaceH p. The main result of this paper is that Kolmogorov, Gelfand, and linearn-widths ofA p inL q are comparable in size to each other and to the sampling error ifq≤p. Moreover, ifp=q=2 andE is small enough, then all these quantities are equal.

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Authors and Affiliations

  1. Department of Mathematics, Northwestern University, 60208, Evanston, Illinois, USA

    S. D. Fisher

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  1. S. D. Fisher
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Communicated by Stephan Ruscheweyh.

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Fisher, S.D. Widths and optimal sampling in spaces of analytic functions. Constr. Approx 12, 463–480 (1996). https://doi.org/10.1007/BF02437503

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  • DOI: https://doi.org/10.1007/BF02437503

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