Title: The role of the endpoint in weighted polynomial approximation with varying weights
Authors: Kuijlaars, Arno # ×
Issue Date: 1996
Series Title: Constructive approximation vol:12 issue:2 pages:287-301
Abstract: For a weight function w: [a, b] -> (0, infinity), we consider weighted polynomials of the form w^n P_n where the degree of P_n is at most n. The class of functions that can be approximated with such polynomials depends on the behavior of the density v(t) of the extremal measure associated with w. We show that every approximable function must vanish at the endpoint alpha if v(t) behaves like (t - alpha)(beta) as t -> alpha with beta > -1/2. We also present an analogous result for internal points. Our results solve some open problems posed by V. Totik and disprove a conjecture of G. G. Lorentz on incomplete polynomials.
ISSN: 0176-4276
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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