Inequalities of Rafalson type for algebraic polynomials

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For a positive Borel measure dmu, we prove that the constant gamma(n) (dv; dy) := (pi is an element ofPn\{0})sup integral-(infinity)(infinity) pi(2) (x)dmu(x)/<(&INT;-(infinity)(&INFIN;))over bar> pi(2) (x) dmu (x), can be represented by the zeros of orthogonal polynomials corresponding to dy in case (i) dv(x) = (A + Bx)dmu(x), where A + Bx is nonnegative on the support of dmu and (ii) dv(x) = (A + Bx(2))dmu(x), where dy is symmetric and A + Bx(2) is nonnegative on the support of dy. The extremal polynomials attaining the constant are obtained and some concrete examples are given including Markov-type inequality when dy is a measure for Jacobi polynomials. (C) 2004 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2004-06
Language
English
Article Type
Article
Citation

JOURNAL OF APPROXIMATION THEORY, v.128, pp.175 - 186

ISSN
0021-9045
DOI
10.1016/j.jat.2004.04.009
URI
http://hdl.handle.net/10203/82170
Appears in Collection
MA-Journal Papers(저널논문)
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