A differential version of the Chebyshev-Markov-Stieltjes inequalities

Shoni Gilboa; Ron Peled

doi:10.1016/j.jat.2015.02.010

A differential version of the Chebyshev-Markov-Stieltjes inequalities

Shoni Gilboa, Ron Peled

Mathematics discipline

Research output: Contribution to journal › Article › peer-review

Abstract

We show that a differential version of the classical Chebyshev-Markov-Stieltjes inequalities holds for a broad family of weight functions. Such a differential version appears to be new. Our results apply to weight functions which are bounded away from zero and piecewise absolutely continuous and yield effective estimates when the weight satisfies additional regularity conditions.

Original language	English
Pages (from-to)	13-54
Number of pages	42
Journal	Journal of Approximation Theory
Volume	196
DOIs	https://doi.org/10.1016/j.jat.2015.02.010
State	Published - 1 Aug 2015

Bibliographical note

Funding Information:
We thank Vladimir Badkov, Percy Deift, Eli Levin, Doron Lubinsky, Paul Nevai and Mikhail Sodin for helpful remarks and discussions during the course of this work. The second author was supported by ISF grant 1048/11 and IRG grant SPTRF .

Publisher Copyright:
© 2015 Elsevier Inc.

Keywords

Canonical representations
Chebyshev-Markov-Stieltjes inequalities
Christoffel function
Moment problem
Orthogonal polynomials
Quadrature formulas

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10.1016/j.jat.2015.02.010

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KW - Orthogonal polynomials

KW - Quadrature formulas

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A differential version of the Chebyshev-Markov-Stieltjes inequalities

Abstract

Bibliographical note

Keywords

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