Total nonnegativity of infinite Hurwitz matrices of entire and meromorphic functions

Abstract

In this paper we fully describe functions generating the infinite totally nonnegative Hurwitz matrices. In particular, we generalize the well-known result by Asner and Kemperman on the total nonnegativity of the Hurwitz matrices of real stable polynomials. An alternative criterion for entire functions to generate a Pólya frequency sequence is also obtained. The results are based on a connection between a factorization of totally nonnegative matrices of the Hurwitz type and the expansion of Stieltjes meromorphic functions into Stieltjes continued fractions (regular $C$-fractions with positive coefficients).

References in corpus (2)

• Structured matrices, continued fractions, and root localization of polynomials
• Hermite-Biehler, Routh-Hurwitz, and total positivity

Cited by in corpus (4)

• Total positivity of some polynomial matrices that enumerate labeled trees and forests, I. Forests of rooted labeled trees
• Total nonnegativity of finite Hurwitz matrices and root location of polynomials
• Hurwitz matrices of doubly infinite series
• Self-interlacing polynomials