2016/11/28 by Tyaglov, Mikhail
#12D10 #15B05 #26C10 #26C15 #30C15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.1611.09156
We describe a new subclass of the class of real polynomials with real simple roots called self-interlacing polynomials. This subclass is isomorphic to the class of real Hurwitz stable polynomials (all roots in the open left half-plane). In the work, we present basic properties of self-interlacing polynomials and their relations with Hurwitz and Hankel matrices as well as with Stiltjes type of continued fractions. We also establish "self-interlacing" analogues of the well-known Hurwitz and Liénard-Chipart criterions for stable polynomials. A criterion of Hurwitz stability of polynomials in terms of minors of certain Hankel matrices is established.