Imaginary projections: Complex versus real coefficients

Properties of conically stable polynomials and imaginary projections

“…This thesis is based on the articles [32,36,42] and the author's contributions to these articles are stated in this section.…”

“…A polynomial f ∈ C[z] is called conically stable if the imaginary parts of the roots of f do not lie in the relative interior of some real cone. In this thesis and the related articles [32,36,42], we derive the following results for conically stable polynomials and related concepts:…”

“…This thesis is based on [32,36,42, see also Appendix A-C] and structured as follows: Firstly, a brief overview of several concepts which generalize real-rootedness is given in Section 2. This section also introduces necessary definitions and notations.…”

“…[42, Lemma 4.1] Under the action of G n , any quadratic polynomial f ∈ C[z] with hyperbolic initial form can be transformed to one of the following normal forms:…”

“…[42, Corollary 4.6] Let f ∈ C[z] be a quadratic polynomial with hyperbolic initial form. Then(1) the complement I(f ) c is either empty or it consists of -one, two, three, or four unbounded components, -two unbounded components and a single point.…”