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arXiv · 1707.05202

Zeros of exceptional orthogonal polynomials and the maximum of the modulus of an energy function

Yu Luo
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Abstract

We propose a new property of the zeros of exceptional orthogonal polynomials. It has been known that exceptional orthogonal polynomials (XOP) have both real and complex zeros. By fixing m variables at the imaginary parts of the complex zeros of XOP, we find that in some cases the modulus of the energy function of a many-particle system attains its maximum at the zeros of XOP. We give a sufficient condition for this result with respect to the denominators of the weight function of XOP.

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Yu Luo. 2017-06-24. Zeros of exceptional orthogonal polynomials and the maximum of the modulus of an energy function. https://arxiv.org/abs/1707.05202

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