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Orthogonal Polynomials
In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.
Logarithmic Potentials with External Fields
This treatment of potential theory emphasizes the effects of an external field (or weight) on the minimum energy problem. Several important aspects of the external field problem (and its extension to
Moduli of smoothness
The book introduces a new way of measuring smoothness. The need for this new concept arises from the failure of the classical moduli of smoothness to solve some basic problems, such as characterizing
General Orthogonal Polynomials
Introduction 1. Upper and lower bounds 2. Zero distribution of orthogonal polynomials 3. Regular n-th root asymptotic behaviour of orthogonal polynomials 4. Regularity criteria 5. Localization 6.
Asymptotics for Christoffel functions for general measures on the real line
We consider asymptotics of Christoffel functions for measures ν with compact support on the real line. It is shown that under some natural conditionsn times thenth Christoffel function has a limit
Weighted Polynomial Inequalities with Doubling and A∞ Weights
Abstract. We consider weighted inequalities such as Bernstein, Nikolskii, Remez, etc., inequalities under minimal assumptions on the weights. It turns out that in most cases this mimimal assumption
Szegö’s extremum problem on the unit circle
It is shown that the Christoffel functions arising from the Szegd extremum problem associated with a finite positive Borel measure on the interval [- wr, wr) satisfy
Polynomial inverse images and polynomial inequalities
valid for polynomials Pn of degree at most n. In this paper we are primarily interested in what form these inequalities take on several intervals. We shall see that the extension to general sets
Universality and fine zero spacing on general sets
A recent approach of D. S. Lubinsky yields universality in random matrix theory and fine zero spacing of orthogonal polynomials under very mild hypothesis on the weight function, provided the support