Interlacing of zeros of orthogonal polynomials under modification of the measure

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• 作者：Dimitar K. Dimitrov ; Mourad E.H. Ismail ; Fern ; o R. Rafaeli
• 关键词：Orthogonal polynomials ; Classical orthogonal polynomials ; qq-orthogonal polynomials ; Zeros ; Interlacing ; Monotonicity
• 刊名：Journal of Approximation Theory
• 出版年：2013
• 出版时间：November, 2013
• 年：2013
• 卷：175
• 期：Complete
• 页码：64-76
• 全文大小：210 K

文摘

We investigate the mutual location of the zeros of two families of orthogonal polynomials. One of the families is orthogonal with respect to the measure , supported on the interval and the other with respect to the measure , where and are outside . We prove that the zeros of these polynomials, if they are of equal or consecutive degrees, interlace when either or and . This result is inspired by an open question of Richard Askey and it generalizes recent results on some families of orthogonal polynomials. Moreover, we obtain further statements on interlacing of zeros of specific orthogonal polynomials, such as the Askey-Wilson ones.