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Specific examples of exponential weights. (English) Zbl 1168.41305
Summary: Let Q 2 :[0,) be an even function. Then we will consider the exponential weights w(x)=exp(-Q(x)) in the weight class from E. Levin and D. S. Lubinsky [Orthogonal polynomials for exponential weights, Springer, New York (2001; Zbl 0997.42011)]. In the paper, we will give some relations among exponential weights in this class and introduce a new weight subclass. In addition, we will investigate some properties of the typical and specific weights in these weight classes.
MSC:
41A10Approximation by polynomials
41A17Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities)