高度表
发表于 2025-3-25 03:39:51
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Celiac-Plexus
发表于 2025-3-25 08:51:33
Restricted Range Inequalities,We have already seen that for . convex, and not identically vanishing polynomials . of degree ≦ ., there holds the Mhaskar-Saff inequality:
ingestion
发表于 2025-3-25 12:31:40
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
发表于 2025-3-25 19:09:09
,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
发表于 2025-3-25 23:26:01
Christoffel Functions,Christoffel functions are crucially important in analysis of orthogonal poly-nomials and weighted approximation theory . 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
发表于 2025-3-26 02:32:37
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
发表于 2025-3-26 05:25:12
Zeros of Orthogonal Polynomials,Recall that given a weight .. on the finite or infinite interval ., its .th orthonormal polynomial .. (..,.) has zeros ., where
粗野
发表于 2025-3-26 12:03:46
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
发表于 2025-3-26 16:09:36
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 and also .
Ccu106
发表于 2025-3-26 18:48:38
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