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 Rfr
ⁿ
times RfrrarrRfr
ⁿ
maps an arbitrary stable polytope into another stable polytope. The second transformation Rfr
ⁿ
times RfrrarrRfr
ⁿ
maps a stable tilted n-dimensional hyperrectangle defined by the discrete Kharitonov theorem into a stable (n+1)- dimensional polytope.