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arXiv · 1312.4376

Zero distribution of complex orthogonal polynomials with respect to exponential weights

Daan Huybrechs·Arno Kuijlaars·Nele Lejon
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Abstract

We study the limiting zero distribution of orthogonal polynomials with respect to some particular exponential weights exp(-nV(z)) along contours in the complex plane. We are especially interested in the question under which circumstances the zeros of the orthogonal polynomials accumulate on a single analytic arc (one cut case), and in which cases they do not. In a family of cubic polynomial potentials V(z) = - iz^3/3 + iKz, we determine the precise values of K for which we have the one cut case. We also prove the one cut case for a monomial quintic V(z) = - iz^5/5 on a contour that is symmetric in the imaginary axis.

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Daan Huybrechs, Arno Kuijlaars, Nele Lejon. 2013-12-16. Zero distribution of complex orthogonal polynomials with respect to exponential weights. https://arxiv.org/abs/1312.4376

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