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Publication Details
AFRICAN RESEARCH NEXUS
SHINING A SPOTLIGHT ON AFRICAN RESEARCH
mathematics
The weighted L
p
-norms of orthonormal polynomials for freud weights
Journal of Approximation Theory, Volume 77, No. 1, Year 1994
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Description
Let W(colon equals) e-Q, where Q: R → R is even, continuous in R, Q" is continuous in (0, ∞), and Q′ > 0 in (0, ∞), while for some A, B > 1, [formula]. For example, W(x) = exp(-|x|α), α > 1, satisfies these hypotheses. Let pn(W2, x) denote the nth orthonormal polynomial for the weight W2, n ≥ 1, and let an = an(Q) denote the nth Mhaskar-Rahmanov-Saff number for Q. We show that for 0 < p < ∞, and n ≥ 2, [formula] The results are based on bounds for pn(W2,.) established recently by A. L. Levin and one of the authors. © 1994 Academic Press, Inc.
Authors & Co-Authors
Lubinsky, Doron S.
South Africa, Johannesburg
University of the Witwatersrand
Móricz, F.
Hungary, Szeged
University of Szeged Bolyai Institute
Statistics
Citations: 26
Authors: 2
Affiliations: 2
Identifiers
Doi:
10.1006/jath.1994.1032
ISSN:
00219045