Reflection Coefficients of Polynomials and Stable Polytopes

The geometry of stable discrete polynomials using their coefficients and reflection coefficients is investigated. Two linear Schur invariant transformations with a free parameter in the polynomial coefficient space are introduced. The first transformation Rfrⁿ times RfrrarrRfrⁿ maps an arbitrary stable polytope into another stable polytope. The second transformation Rfrⁿ times RfrrarrRfrⁿ maps a stable tilted n-dimensional hyperrectangle defined by the discrete Kharitonov theorem into a stable (n+1)- dimensional polytope.