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 |
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Pages (from-to) | 13-54 |
Number of pages | 42 |
Journal | Journal of Approximation Theory |
Volume | 196 |
DOIs | |
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