Linear operators on polynomials preserving roots in open circular domains

2011/11/09 by Eugeny Melamud, Melamud, Eugeny
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematics and Applications #Rings, Modules, and Algebras #math.CV

paper · pdf · doi:10.48550/arxiv.1111.2209

6 pages

arxiv created 2011/11/09 · openalex publication_date 2011/11/09 · arxiv updated 2011/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper we answer a question raised by J. Borcea and P. Branden 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 Mobius transformations. Our second result is a description of the difference between \Apr(G) (the class of operators preserving roots in an open set G) and \Apr( G) (the class of operators preserving roots in G).

Related

• A Representation Theoretic Explanation of the Borcea-Brändén Characterization
• Preserving positive polynomials and beyond
• Polynomials, roots, and interlacing
• On the linearity of origin-preserving automorphisms of quasi-circular domains in \mathbb Cⁿ
• On automorphisms of quasi-circular domains fixing the origin