关于精确可解微分算子的多项式特征函数的渐近性
On Asymptotics of Polynomial Eigenfunctions for Exactly-Solvable Differential Operators
摘要：
本文研究退化正解算子本征多项式的渐近零分布。我们提出了一个明确的猜想和部分结果的增长的最大模的根的唯一和monic n：th度本征多项式的任何这样的运营商的程度n趋于无穷大。基于这个猜想，我们导出了适当尺度特征多项式的渐近根测度的Cauchy变换所满足的代数方程，其中所有根的并严格包含在一个紧集中.
英文摘要：
In this paper we study the asymptotic zero distribution of eigenpolynomials for degenerate exactly-solvable operators. We present an explicit conjecture and partial results on the growth of the largest modulus of the roots of the unique and monic n:th degree eigenpolynomial of any such operator as the degree n tends to infinity. Based on this conjecture we deduce the algebraic equation satified by the Cauchy transform of the asymptotic root measure of the properly scaled eigenpolynomials, for which the union of all roots is conjecturally contained in a compact set.
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