Berlin Technical University
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.