The Lee-Yang and Pólya-Schur programs. I. Linear operators preserving stability
2009 (English)In: Inventiones Mathematicae, ISSN 0020-9910, E-ISSN 1432-1297, Vol. 177, no 3, 541-569 p.Article in journal (Refereed) Published
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.
IdentifiersURN: urn:nbn:se:su:diva-35119DOI: 10.1007/s00222-009-0189-3ISI: 000268951100004OAI: oai:DiVA.org:su-35119DiVA: diva2:286448