Reflection Coefficients of Polynomials and Stable Polytopes |
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Abstract: | 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 ${cal R}^{n}times{cal R}rightarrow{cal R}^{n}$ maps an arbitrary stable polytope into another stable polytope. The second transformation ${cal R}^{n}times{cal R}rightarrow{cal R}^{n+1}$ maps a stable tilted $n$-dimensional hyperrectangle defined by the discrete Kharitonov theorem into a stable $(n+1)$- dimensional polytope. |
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