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Asymptotics of polynomials orthogonal over circular multiply connected domains
Journal of Approximation Theory ( IF 0.9 ) Pub Date : 2019-12-05 , DOI: 10.1016/j.jat.2019.105347
James Henegan , Erwin Miña-Díaz

Let D be a domain obtained by removing, out of the unit disk {z:|z|<1}, finitely many mutually disjoint closed disks, and for each integer n0, let Pn(z)=zn+ be the monic nth-degree polynomial satisfying the planar orthogonality condition DPn(z)zm¯dxdy=0, 0m<n. Under a certain assumption on the domain D, we establish asymptotic expansions and formulae that describe the behavior of Pn(z) as n at every point z of the complex plane. We also give an asymptotic expansion for the squared norm D|Pn|2dxdy.



中文翻译:

在圆形多重连接域上正交的多项式的渐近性

d 是通过从单位磁盘中删除而获得的域 {ž|ž|<1个},有限多个相互不相交的封闭磁盘,并且对于每个整数 ñ0,让 Pñž=žñ+ 成为莫妮卡 ñ满足平面正交性条件的三次多项式 dPñžž¯dXdÿ=00<ñ。在域的一定假设下d,我们建立了渐近展开和公式来描述行为 Pñžñ 在每一点上 ž复杂平面的 我们还给出平方范数的渐近展开d|Pñ|2dXdÿ

更新日期:2019-12-05
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