Geometry of convex sets arising from hyperbolic polynomials
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This thesis focuses on convex sets and convex cones defined using hyperbolic polynomials. We first review some of the theory of convex sets in $\R^d$ in general. We then review some classical algebraic theorems concerning polynomials in a single variable, as well as presenting a few more modern results about them. We then discuss the theory of hyperbolic polynomials in several variables and their associated hyperbolicity cones. We survey various ways to build and decompose hyperbolic cones and we prove that every nontrivial hyperbolic cone is the intersection of its derivative cones. We conclude with a brief discussion of the set of extreme rays of a hyperbolic cone.
Cite this version of the work
Tor Gunnar Josefsson Jay Myklebust (2008). Geometry of convex sets arising from hyperbolic polynomials. UWSpace. http://hdl.handle.net/10012/3960