Generalized Hurwitz polynomials

Abstract

We describe a wide class of polynomials, which is a natural generalization of Hurwitz stable polynomials. We also give a detailed account of so-called self-interlacing polynomials, which are dual to Hurwitz stable polynomials but have only real and simple zeroes. All proofs are given using properties of rational functions mapping the upper half-plane of the complex plane to the lower half-plane. Matrices with self-interlacing spectra and other applications of generalized Hurwitz polynomials are discussed.

59 pages

References in corpus (1)

• Polynomials, roots, and interlacing

Cited by in corpus (1)

• Positivity of Toeplitz determinants formed by rising factorial series and properties of related polynomials