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Linear operators on polynomials preserving roots in open circular domains


Author: Eugeny Melamud
Journal: Proc. Amer. Math. Soc. 143 (2015), 5213-5218
MSC (2010): Primary 30C15; Secondary 32A60, 47B38
DOI: https://doi.org/10.1090/proc/12109
Published electronically: August 12, 2015
MathSciNet review: 3411138
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Abstract: In the present paper we answer a question raised by J. Borcea and P. Brändén and give a description of the class of operators preserving roots in open circular domains, i.e., in images of the open upper half-plane under the Möbius transformations. Our second result is a description of the difference between $ \mathcal A(G)$ (the class of operators preserving roots in an open set $ G$) and $ \mathcal A(\overline G)$ (the class of operators preserving roots in $ \overline {G}$).


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Eugeny Melamud
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, 28, Universitetskii pr., St. Petersburg, 198504, Russia
Email: eugeny.melamud@comapping.com

DOI: https://doi.org/10.1090/proc/12109
Keywords: Linear operators on polynomial spaces, zeros of polynomials, circular domains, P\'olya--Schur theorem
Received by editor(s): November 30, 2011
Received by editor(s) in revised form: December 1, 2012
Published electronically: August 12, 2015
Communicated by: Richard Rochberg
Article copyright: © Copyright 2015 American Mathematical Society