Geodesics, Retracts, and the Norm-Preserving Extension Property in the Symmetrized Bidisc
A set
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| Hlavní autoři: | , , |
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| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
| Vydáno: |
Providence, Rhode Island
American Mathematical Society
2019
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| Vydání: | 1 |
| Edice: | Memoirs of the American Mathematical Society |
| Témata: | |
| ISBN: | 9781470435493, 1470435497 |
| ISSN: | 0065-9266, 1947-6221 |
| On-line přístup: | Získat plný text |
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- Preface -- Introduction -- An overview -- Extremal problems in the symmetrized bidisc <inline-formula content-type="math/mathml"> G G </inline-formula> -- Complex geodesics in <inline-formula content-type="math/mathml"> G G </inline-formula> -- The retracts of <inline-formula content-type="math/mathml"> G G </inline-formula> and the bidisc <inline-formula content-type="math/mathml"> D 2 \mathbb {D}^2 </inline-formula> -- Purely unbalanced and exceptional datums in <inline-formula content-type="math/mathml"> G G </inline-formula> -- A geometric classification of geodesics in <inline-formula content-type="math/mathml"> G G </inline-formula> -- Balanced geodesics in <inline-formula content-type="math/mathml"> G G </inline-formula> -- Geodesics and sets <inline-formula content-type="math/mathml"> V V </inline-formula> with the norm-preserving extension property in <inline-formula content-type="math/mathml"> G G </inline-formula> -- Anomalous sets <inline-formula content-type="math/mathml"> R ∪ D \mathcal {R}\cup \mathcal {D} </inline-formula> with the norm-preserving extension property in <inline-formula content-type="math/mathml"> G G </inline-formula> -- <inline-formula content-type="math/mathml"> V V </inline-formula> and a circular region <inline-formula content-type="math/mathml"> R R </inline-formula> in the plane -- Proof of the main theorem -- Sets in <inline-formula content-type="math/mathml"> D 2 \mathbb {D}^2 </inline-formula> with the symmetric extension property -- Applications to the theory of spectral sets -- Anomalous sets with the norm-preserving extension property in some other domains -- Some useful facts about the symmetrized bidisc -- Types of geodesic: a crib and some cartoons
- 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