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The Lee-Yang and Pólya-Schur programs. I. Linear operators preserving stability.
- Source :
-
Inventiones Mathematicae . Sep2009, Vol. 177 Issue 3, p541-569. 29p. - Publication Year :
- 2009
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00209910
- Volume :
- 177
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Inventiones Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 43534948
- Full Text :
- https://doi.org/10.1007/s00222-009-0189-3