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The Lee-Yang and Pólya-Schur programs: II. Theory of stable polynomials and applications
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
2009 (English)In: Communications on Pure and Applied Mathematics, ISSN 0010-3640, E-ISSN 1097-0312, Vol. 62, no 12, 1595-1631 p.Article in journal (Refereed) Published
Abstract [en]

In the first part of this series we characterized all linear operators on spaces of multivariate polynomials preserving the property of being nonvanishing in products of open circular domains. For such sets this completes the multivariate generalization of the classification program initiated by Pólya and Schur for univariate real polynomials. We build on these classification theorems to develop here a theory of multivariate stable polynomials. Applications and examples show that this theory provides a natural framework for dealing in a uniform way with Lee-Yang type problems in statistical mechanics, combinatorics, and geometric function theory in one or several variables. In particular, we answer a question of Hinkkanen on multivariate apolarity.

Place, publisher, year, edition, pages
2009. Vol. 62, no 12, 1595-1631 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-35123DOI: 10.1002/cpa.20295ISI: 000271299700001OAI: oai:DiVA.org:su-35123DiVA: diva2:286456
Available from: 2010-01-14 Created: 2010-01-14 Last updated: 2017-12-12Bibliographically approved

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