Communications on pure and applied mathematics, 2009-12, Vol.62 (12), p.1595-1631
2009
Details
- Autor(en) / Beteiligte
- Titel
- The Lee-Yang and Pólya-Schur programs. II. Theory of stable polynomials and applications
- Ist Teil von
- Communications on pure and applied mathematics, 2009-12, Vol.62 (12), p.1595-1631
- Ort / Verlag
- Hoboken: Wiley Subscription Services, Inc., A Wiley Company
- Erscheinungsjahr
- 2009
- Link zum Volltext
- Quelle
- Wiley Online Library - AutoHoldings Journals
- Beschreibungen/Notizen
- 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. © 2009 Wiley Periodicals, Inc.
- Sprache
- Englisch
- Identifikatoren
- ISSN: 0010-3640, 1097-0312eISSN: 1097-0312DOI: 10.1002/cpa.20295Titel-ID: cdi_swepub_primary_oai_DiVA_org_su_35123
- Format
- –
- Schlagworte
- 1st-order phase-transitions, algebraic equations, brownian intersection exponents, Combinatorics, Combinatorics. Ordered structures, Exact sciences and technology, ferromagnets, Functional analysis, Functions of a complex variable, half-plane property, invariant-theory, MATEMATIK, Mathematical analysis, MATHEMATICS, multiplier, Operator theory, partition-function zeros, real zeros, Sciences and techniques of general use, sequences, systems