Titlebook: Orthogonal Polynomials for Exponential Weights; Eli Levin,Doron S. Lubinsky Textbook 2001 Springer-Verlag New York, Inc. 2001 Smooth funct

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Celiac-Plexus

Restricted Range Inequalities,We have already seen that for . convex, and not identically vanishing polynomials . of degree ≦ ., there holds the Mhaskar-Saff inequality:

ingestion

Estimates for Measure and Potential,In this chapter, we obtain upper and lower bounds for the equilibrium density σ.(.) and for the associated potential ... The lower bounds are easy to obtain, and minimal assumptions on . are needed:

Transfusion

,Smoothness of σ,,The smoothness of σ. plays a role in discretising the potential to obtain weighted polynomial approximations. In this chapter, we establish various levels of smoothness of σ. under corresponding conditions on ..

裤子

Christoffel Functions,Christoffel functions are crucially important in analysis of orthogonal poly-nomials and weighted approximation theory [146]. In this chapter we shall estimate generalized and classical .. Christoffel functions for 0 < .≤∞ using the polynomials constructed in Chapter 7. We shall also establish asymptotics for classical Christoffel functions.

针叶树

Markov-Bernstein and Nikolskii Inequalities,In this chapter, we shall prove Markov-Bernstein inequalities and Nikolskii inequalities. We begin with the former. We shall make substantial use of the function ϕ. defined by (9.18) and (9.19).

警告

Zeros of Orthogonal Polynomials,Recall that given a weight .. on the finite or infinite interval ., its .th orthonormal polynomial .. (..,.) has zeros ., where

粗野

Bounds on Orthogonal Polynomials,Perhaps the most significant result of this work is the following uniform bound on the orthogonal polynomials throughout the interval of orthogonality:

善于骗人

Asymptotics of Extremal Polynomials,In this chapter, we establish mean asymptotics on the real line for extremal polynomials, and also their asymptotics in the plane. Our approach follows very closely that in [101] and also [114].

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