Sharp distortion theorems for rational functions without poles or zeros in simply connected domains

DOI10.1080/17476930600785338zbMath1114.30025OpenAlexW2230798447MaRDI QIDQ3426250

Rudolf Rupp

Publication date: 8 March 2007

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476930600785338

zbMATH Keywords

rational functionsdistortion theoremshyperbolic distancesimultaneous stabilizationPoincaré metriczeroes and poles

Mathematics Subject Classification ID

Pole and zero placement problems (93B55) Incompressible inviscid fluids (76B99) Geometric function theory (30C99)

Cites Work

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• Unit interpolation in \(H_{\infty{}}\): Bounds of norm and degree of interpolants
• Simultaneous stabilization of linear systems
• Simultaneous stabilizability of three linear systems is rationally undecidable
• Uniform estimates for the hyperbolic metric and Euclidean distance to the boundary
• Distortion theorems for rational functions without poles or zeros in simply connected domains
• Simultaneous Stabilization of Three or More Plants: Conditions on the Positive Real Axis Do Not Suffice
• On Zero and One Points of Analytic Functions

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