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Lee–Yang Problems and the Geometry of Multivariate Polynomials

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Abstract

We describe all linear operators on spaces of multivariate polynomials preserving the property of being non-vanishing in open circular domains. This completes the multivariate generalization of the classification program initiated by Pólya–Schur for univariate real polynomials and provides a natural framework for dealing in a uniform way with Lee–Yang type problems in statistical mechanics, combinatorics, and geometric function theory.

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Authors and Affiliations

  1. Department of Mathematics, Stockholm University, 106 91, Stockholm, Sweden

    Julius Borcea

  2. Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden

    Petter Brändén

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  1. Julius Borcea
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  2. Petter Brändén
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Correspondence to Julius Borcea.

Additional information

J. Borcea was partially supported by the Swedish Research Council and the Crafoord Foundation. P. Brändén was partially supported by the Göran Gustafsson Foundation.

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Borcea, J., Brändén, P. Lee–Yang Problems and the Geometry of Multivariate Polynomials. Lett Math Phys 86, 53–61 (2008). https://doi.org/10.1007/s11005-008-0271-6

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  • DOI: https://doi.org/10.1007/s11005-008-0271-6

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