Properties of conically stable polynomials and imaginary projections

  • We thoroughly study the properties of conically stable polynomials and imaginary projections. A multivariate complex polynomial is called stable if its nonzero whenever all coordinates of the respective argument have a positive imaginary part. In this dissertation we consider the generalized notion of K-stability. A multivariate complex polynomial is called K-stable if its non-zero whenever the imaginary part of the respective argument lies in the relative interior of the cone K. We study connections to various other objects, including imaginary projections as well as preservers and combinatorial criteria for conically stable polynomials.

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Author:Stephan GardollGND
Place of publication:Frankfurt am Main
Referee:Thorsten TheobaldORCiDGND, Cynthia VinzantORCiD
Advisor:Thorsten Theobald
Document Type:Doctoral Thesis
Date of Publication (online):2023/03/27
Year of first Publication:2022
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Granting Institution:Johann Wolfgang Goethe-Universität
Date of final exam:2023/03/03
Release Date:2023/05/02
Page Number:128
Kumulative Dissertation - enthält die eingereichten Manuskriptversionen (Author Submitted Manuscripts) der folgenden Artikel: 

Dey, Papri; Gardoll, Stephan; Theobald, Thorsten (2020): Conic stability of polynomials and positive maps. arXiv:1908.11124v2, DOI: 10.48550/arXiv.1908.11124

Gardoll, Stephan; Namin, Mahsa Sayyary; Theobald, Thorsten (2022): Imaginary Projections: Complex Versus Real Coefficients. arXiv:2107.08841v3. DOI: 10.48550/arXiv.2107.08841.

Codenotti, Giulia; Gardoll, Stephan; Theobald, Thorsten (2022): Combinatorics and preservation of conically stable polynomials. arXiv:2206.10913v2. DOI:
Institutes:Informatik und Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoDeutsches Urheberrecht