Special Analysis Seminar, Thursday 31st January 2019

Speaker: Mikhail Tyaglov (Shanghai Jiao Tong University)
Title: Tridiagonal matrices, Hankel minors, and special functions
Abstract:
In this survey talk, we discuss some old and new results on the distribution of eigenvalues of certain type tridiagonal matrices and their connections with distribution of zeros of orthogonal polynomials and special function. We consider relations of tridiagonal matrices with Hurwitz stable polynomials and the so-called self-interlacing polynomials that appear in the theory of orthogonal polynomials. We also introduce the so-called Stieltjes, self-interlacing and "strange" moment sequences and give examples of generating functions (or related rational approximants) for each type of sequences. Relations to totally positive sequences will be discussed.

At the end of the talk we will pose some conjectures and open problems on generating fuctions of the aforementioned moment sequences.