# SPECIFIC EXAMPLES OF EXPONENTIAL WEIGHTS

• Published : 2009.04.30

#### Abstract

Let $Q\;{\in}\;C^2$ : ${\mathbb{R}}\;{\rightarrow}\;[0,{\infty})$ be an even function. Then we will consider the exponential weights w(x) = exp(-Q(x)) in the weight class from [2]. 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.

#### References

1. Y. Kanjin and R. Sakai, Pointwise convergence of Hermite-Fejer interpolation of higher order for Freud weights, Tohoku. Math. 46 (1994), 181–206 https://doi.org/10.2748/tmj/1178225757
2. A. L. Levin and D. S. Lubinsky, Orthogonal Polynomials for Exponential Weights, Springer, New York, 2001
3. P. Vertesi, Hermite-Fejer interpolations of higher order. I, Acta Math. Hungar. 54(1989), 135–152 https://doi.org/10.1007/BF01950715

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