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Total Nonnegativity of Hurwitz Matrices for Doubly Infinite Power Series

Speaker

Alexander Dyachenko, Berlin Technical University

Time

2017.03.23 14:00-15:00

Venue

Middle Lecture Room, Math Building

Abstract

During this talk, I am going to answer the question: which functions generate totally nonnegative Hurwitz matrices? In my previous talk, I give the answer suitable for polynomials and entire functions, which does not cover the general case of Hurwitz matrices built from the Laurent series. The main issue is that the essential connection to Hankel matrices breaks in the doubly infinite case (no correspondent Stieltjes continued fraction). I would like to introduce another approach for dealing with this problem. It appears to be helpful to build two certain families of Toeplitz matrices from a totally nonnegative Hurwitz matrix. Studying two relevant families of functions arising from the criterion by Edrei (1953) then allows to establish the explicit form of the function arising from the Hurwitz matrix.