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Specific examples of exponential weights. (English) Zbl 1168.41305
Summary: Let $Q\in {ℂ}^{2}:ℝ\to \left[0,\infty \right)$ be an even function. Then we will consider the exponential weights $w\left(x\right)=exp\left(-Q\left(x\right)\right)$ 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:
 41A10 Approximation by polynomials 41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities)
Keywords:
exponential weights