TY  - BOOK
AU  - Agler,Jim
AU  - Lykova,Zinaida
AU  - Young,Nicholas
TI  - Geodesics, Retracts, and the Norm-Preserving Extension Property in the Symmetrized Bidisc
T2  - Memoirs of the American Mathematical Society Series
SN  - 9781470450755
AV  - QA360 .A354 2019 
U1  - 516.3/62 
PY  - 2019///
CY  - Providence
PB  - American Mathematical Society
KW  - Geometric function theory
KW  - Functions of complex variables
KW  - Geometry, Differential
KW  - Retracts, Theory of
KW  - Hermitian operators
KW  - Electronic books
N1  - Cover -- Title page -- Preface -- Chapter 1. Introduction -- Chapter 2. An overview -- Chapter 3. Extremal problems in the symmetrized bidisc -- 3.1. The Carathéodory and Kobayashi extremal problems -- 3.2. The Carathéodory extremal problem    ( ) for -- 3.3. Five types of datum   in -- 3.4. The Kobayashi extremal problem    ( ) for -- Chapter 4. Complex geodesics in -- 4.1. Complex geodesics and datums in -- 4.2. Uniqueness of complex geodesics for each datum in -- 4.3. Flat C-geodesics -- 4.4. Rational \Ga-inner functions -- Chapter 5. The retracts of   and the bidisc  ² -- 5.1. Retracts and geodesics of -- 5.2. Retracts of  ² -- 5.3. Geodesics in   are varieties -- Chapter 6. Purely unbalanced and exceptional datums in -- Chapter 7. A geometric classification of geodesics in -- Chapter 8. Balanced geodesics in -- Chapter 9. Geodesics and sets   with the norm-preserving extension property in -- 9.1.   and    ( ) -- 9.2.   and balanced datums -- 9.3.   and flat or royal datums -- Chapter 10. Anomalous sets ℛ∪  with the norm-preserving extension property in -- 10.1. Definitions and lemmas -- 10.2. The proof of the norm-preserving extension property for \calr∪\cald -- Chapter 11.   and a circular region   in the plane -- Chapter 12. Proof of the main theorem -- 12.1. Preliminary lemmas -- 12.2.  : →  is analytic on  ⁻ -- 12.3. Degree considerations -- Chapter 13. Sets in  ² with the symmetric extension property -- Chapter 14. Applications to the theory of spectral sets -- Chapter 15. Anomalous sets with the norm-preserving extension property in some other domains -- Appendix A. Some useful facts about the symmetrized bidisc -- A.1. Basic properties of   and Γ -- A.2. Complex C-geodesics in -- A.3. Automorphisms of -- A.4. A trichotomy theorem -- A.5. Datums for which all Φ_{ } are extremal -- Appendix B. Types of geodesic: a crib and some cartoons; B.1. Crib sheet -- B.2. Cartoons -- Bibliography -- Index -- Back Cover
N2  - View the abstract
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5770288
ER  -