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Comptes Rendus Mathématique
Volume 353, n° 1
pages 11-15 (janvier 2015)
Doi : 10.1016/j.crma.2014.10.017
Received : 29 September 2014 ;  accepted : 23 October 2014
A continuous link between the disk and half-plane cases of Grace's theorem
Un lien continu entre les cas du disque et du demi-plan dans le théorème de Grace
 

Martin Lamprecht
 Department of Computer Science and Engineering, European University of Cyprus, Diogenous Str. 6, Engomi, P.O. Box 22006, 1516 Nicosia, Cyprus 

Abstract

We obtain a continuous link between the disk and half-plane cases of Grace's theorem and new, non-circular zero domains that stay invariant under the Schur–Szegő convolution.

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Résumé

On obtient un lien continu entre les cas du disque et du demi-plan dans le théorème de Grace, ainsi que de nouveaux domaines de zéros non cerclés, qui sont invariants par la convolution de Schur–Szegő.

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