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

ISBN-13: 9781470435493 / Angielski / Miękka / 2019 / 108 str.

Jim Agler;Zinaida Lykova;Nicholas Young

Spis treści

• Introduction
• An overview
• Extremal problems in the symmetrized bidisc $G$
• Complex geodesics in $G$
• The retracts of $G$ and the bidisc $\mathbb ^2$
• 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 \cup \mathcal $ with the norm-preserving extension property in $G$
• $V$ and a circular region $R$ in the plane
• Proof of the main theorem
• Sets in $\mathbb ^2$ 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.