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Zeros and logarithmic asymptotics of Sobolev orthogonal polynomials for exponential weights. (English) Zbl 1177.42020

The authors study the problem of location and asymptotics of zeroes of polynomials orthogonal on the half-axis \(\mathbb{R}^1_+\) with respect to the inner product of the weighted Sobolev space \(W^{2,M}(w,\mathbb{R}^1_+)\) with weight of form \(w(x)=x^\gamma e^{\varphi(x)}, \;\gamma>0\). The obtained asymptotics covers in particular the cases of Freud and Erdös weights.

MSC:

42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
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