On the Banach-Mazur Ellipse
V. D. Babev, M. Ivanov, R. Nikolov
TL;DR
This paper offers a new proof characterizing the minimal Banach-Mazur distance ellipse to the unit circle in a normed plane, linking it to contact points, extremal points, and Chebyshev alternance.
Contribution
It introduces a novel proof approach connecting Banach-Mazur ellipses with Chebyshev alternance, enhancing understanding of geometric extremal problems.
Findings
New proof of Ader's characterization of minimal Banach-Mazur ellipses.
Establishes a relation between extremal contact points and Chebyshev alternance.
Provides insights into geometric optimization in normed planes.
Abstract
We provide a new proof of Ader's characterisation of the ellipse of minimal Banach-Mazur distance to the unit circle of a normed plane in terms of contact and extremal points. Our method reveals the relation of this problem to the Chebyshev alternance.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Geometric and Algebraic Topology