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E-raamat: Geodesics, Retracts, and the Norm-Preserving Extension Property in the Symmetrized Bidisc

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Geodesics, Retracts, and the Norm-Preserving Extension Property in the Symmetrized BidiscSuurem pilt
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Agler, Lykova, and Young determine the holomorphic retractions of the symmetrized bidisc and its subsets, which permit the extension of holomorphic functions without an increase of the supremum norm. The methods they use are of independent interest, they say, and they analyze the complex geodesics of the symmetrized bidisc, and show that there are five qualitatively different types of them. Their topics include extremal problems in the symmetrized bidisc, purely unbalanced and exceptional datums, geodesics and sets with the norm-preserving extension property, proof of the main theorem, and applications to the theory of spectral sets. Annotation ©2019 Ringgold, Inc., Portland, OR (protoview.com)
Introduction
An overview
Extremal problems in the symmetrized bidisc $G$
Complex geodesics in $G$
The retracts of $G$ and the bidisc $\mathbb {D}^2$
Purely unbalanced and exceptional datums in $G$
A geometric classification of geodesics in $G$
Balanced geodesics in $G$
Geodesics and sets $V$ with the norm-preserving extension property in $G$
Anomalous sets $\mathcal {R}\cup \mathcal {D}$ with the norm-preserving
extension property in $G$
$V$ and a circular region $R$ in the plane
Proof of the main theorem
Sets in $\mathbb {D}^2$ with the symmetric extension property
Applications to the theory of spectral sets
Anomalous sets with the norm-preserving extension property in some other
domains
Appendix A. Some useful facts about the symmetrized bidisc
Appendix B. Types of geodesic: a crib and some cartoons
Bibliography
Index.
Jim Agler, University of California at San Diego, CA.

Zinaida Lykova, Newcastle University, Newcastle upon Tyne, United Kingdom.

Nicholas Young, Newcastle University, Newcastle upon Tyne, United Kingdom.
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