Geodesic
Pólya-Schur master theorems for circular domains and their boundaries
Julius Borcea1 ; Petter Brändén2
1 Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden
2 Department of Mathematics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
Annals of mathematics, Tome 170 (2009) no. 1, pp. 465-492.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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 $\Omega\subseteq \mathbb{C}$ for arbitrary closed circular domains $\Omega$ (i.e., images of the closed unit disk under a Möbius transformation) and their boundaries. This provides a natural framework for dealing with several long-standing fundamental problems, which we solve in a unified way. In particular, for $\Omega=\mathbb{R}$ our results settle open questions that go back to Laguerre and Pólya-Schur.
DOI : 10.4007/annals.2009.170.465

Julius Borcea 1 ; Petter Brändén 2

1 Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden
2 Department of Mathematics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden 
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Julius Borcea; Petter Brändén. Pólya-Schur master theorems for circular domains and their boundaries. Annals of mathematics, Tome 170 (2009) no. 1, pp. 465-492. doi : 10.4007/annals.2009.170.465. http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.465/

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