题目：Doubly Infinite Jacobi Matrices Revisited: Resolvent and Spectral Measure
报告人：代丹 副教授（香港城市大学）
地点：宁静楼108室
时间：12月13日（星期三），下午1:00-2:00
个人简介：代丹，香港城市大学副教授，2002年于复旦大学获学士学位，2006年于香港城市大学获博士学位，毕业后曾在比利时鲁汶大学任博士后研究员，师从著名数学家Arno Kuijlaars。主要研究包括渐近分析、随机矩阵和特殊函数等，在Nonlinearity, Constructive Approximations, Communications in Mathematical Physics, Studies in Applied Mathematics, 和Journal of Approximation Theory等国际学术期刊上发表论文二十余篇。
报告摘要
We study the resolvent and spectral measure of certain doubly infinite Jacobi matrices via asymptotic solutions of two-sided difference equations. By finding the subdominant (or minimal) solutions or calculating the continued fractions for the difference equations, we derive explicit formulas for the matrix entries of resolvent of doubly infinite Jacobi matrices corresponding to Lommel polynomials, associated ultraspherical polynomials, and Al-Salam-Ismail polynomials. The spectral measures are then obtained by inverting Stieltjes transformations.
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