Small values of polynomials
and potentials with normalization
Author:
D. S. Lubinsky
Journal:
Proc. Amer. Math. Soc. 127 (1999), 529-536
MSC (1991):
Primary 30C10, 31A15; Secondary 41A17, 41A44, 30C85
DOI:
https://doi.org/10.1090/S0002-9939-99-04549-9
MathSciNet review:
1468199
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: For a polynomial of degree
, normalized by the condition
we show that has
at most
, where
is explicitly given and sharp for each
. Similar estimates are given for other normalizations, such as
, and for planar measure, and for generalized polynomials and potentials, thereby extending work of Cuyt, Driver and the author for
. The relation to Remez inequalities is briefly discussed.
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Additional Information
D. S. Lubinsky
Affiliation:
Department of Mathematics, Witwatersrand University, Wits 2050, South Africa
Email:
036dsl@cosmos.wits.ac.za
DOI:
https://doi.org/10.1090/S0002-9939-99-04549-9
Keywords:
Cartan's lemma, capacity, polynomials, $L_p$ norm
Received by editor(s):
July 17, 1996
Received by editor(s) in revised form:
June 2, 1997
Communicated by:
J. Marshall Ash
Article copyright:
© Copyright 1999
American Mathematical Society