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  1. ; ; ; (, Bulletin of the London Mathematical Society)
    Abstract Given a polynomial with no zeros in the polydisk, or equivalently the poly‐upper half‐plane, we study the problem of determining the ideal of polynomials with the property that the rational function is bounded near a boundary zero of . We give a complete description of this ideal of numerators in the case where the zero set of is smooth and satisfies a nondegeneracy condition. We also give a description of the ideal in terms of an integral closure when has an isolated zero on the distinguished boundary. Constructions of multivariate stable polynomials are presented to illustrate sharpness of our results and necessity of our assumptions. 
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  2. ; ; ; (, Annales Polonici Mathematici)
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