Polya-Schur master theorems for circular domains and their boundaries

By Julius Borcea, Petter Brand'en. 2006

143 citations recorded by the source corpus.

We characterize all linear operators on finite or infinite-dimensional polynomial spaces that preserve the property of having the zero set inside a prescribed region Omega subset of C for arbitrary ...

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d0d585d4b35ba673dfe92455608124ee6e6fad4a

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Citations in the corpus

Applications of stable polynomials to mixed determinants: Johnson's conjectures, unimodality, and symmetrized Fischer products (2006, methodology): “In §4 we apply the theory of real stable polynomials developed in [3, 4, 6] and the present paper to derive Laguerre type inequalities for characteristic polynomials of principal submatrices of arbitrary Hermitian matrices (Theorem 4.1 and Corollary 4.2).”
The Lee-Yang and Pólya-Schur programs. I. Linear operators preserving stability (2008, background): “This dichotomy stems from “soft-core” vs. “hard-core” pair interactions in lattice-gas models and does not refer to the level of difficulty in proving such theorems but rather to the fact that in some sense “soft” theorems are constraint-free while “hard” theorems involve constraints of various…”
Multivariate stable polynomials: theory and applications (2009, background): “h that for each f 2E, P f(t) 2R[[t]] is dominated coecientwise by exp((LN K)t). Thus exp(tL) 2A[[t]] converges for all t0. The semigroup of transformations generated by L is exp(tL). To check claim (3) we will show that the semigroup T(t) of the SEP preserves stability for all t0: that is, if Z(’ 0)”
Multivariate Pólya–Schur classification problems in the Weyl algebra (2006, background): “Further recent contributions include [9], where a complete classification of linear preservers of univariate polynomials with only real zeros — and, more generally, of univariate polynomials with zeros only in a closed circular domain or on the boundary of such a domain — has been obtained, thus sol”
Negative dependence and the geometry of polynomials (2007, methodology): “Polynomials of the aforementioned types are widely encountered in both mathematics and physics [3, 12, 7 , 8, 9, 10, 15, 19, 36, 37, 51] (see also §4.1).”
Iterated sequences and the geometry of zeros (2009, methodology): “Similar characterizations of classes of transformations were given in [12] and [1].”
Unimodality, log-concavity, real-rootedness and beyond (2015, background): “t (2) of Theorem 7.1 is satised, and thus is a multiplier sequence. Only recently a complete characterization of linear operators preserving real{ rootedness was obtained by Borcea and the author in [10]. This characterization is 18 PETTER BRAND EN in terms of a natural extension of real{rootedness ”