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The Lee-Yang and Pólya-Schur programs. I. Linear operators preserving stability
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
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 Pólya-Schur on univariate polynomials with such properties.

Place, publisher, year, edition, pages
2009. Vol. 177, no 3, 541-569 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-35119DOI: 10.1007/s00222-009-0189-3ISI: 000268951100004OAI: oai:DiVA.org:su-35119DiVA: diva2:286448
Available from: 2010-01-14 Created: 2010-01-14 Last updated: 2011-04-07Bibliographically approved

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