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The Lee-Yang and Polya-Schur programs. I. Linear operators preserving stability
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-1055-1474
2009 (English)In: Inventiones Mathematicae, ISSN 0020-9910, E-ISSN 1432-1297, Vol. 177, no 3, 541-569 p.Article in journal (Refereed) Published
Abstract [en]

In 1952 Lee and Yang proposed the program of analyzing phase transitions in terms of zeros of partition functions. Linear operators preserving non-vanishing properties are essential in this program and various contexts in complex analysis, probability theory, combinatorics, and matrix theory. We characterize all linear operators on finite or infinite-dimensional spaces of multivariate polynomials preserving the property of being non-vanishing whenever the variables are in prescribed open circular domains. In particular, this solves the higher dimensional counterpart of a long-standing classification problem originating from classical works of Hermite, Laguerre, Hurwitz and Polya-Schur on univariate polynomials with such properties.

Place, publisher, year, edition, pages
2009. Vol. 177, no 3, 541-569 p.
Keyword [en]
1st-order phase-transitions, partition-function zeros, half-plane, property, algebraic equations, polynomials, theorem, ferromagnets, sequences, systems, roots
URN: urn:nbn:se:kth:diva-18688DOI: 10.1007/s00222-009-0189-3ISI: 000268951100004ScopusID: 2-s2.0-70350649060OAI: diva2:336735
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2010-12-15Bibliographically approved

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Bränden, Petter
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