Finite Blaschke Products and Their Connections
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ISBN-13:
9783319782461
Veröffentl:
2018
Einband:
HC runder Rücken kaschiert
Erscheinungsdatum:
05.06.2018
Seiten:
348
Autor:
Stephan Ramon Garcia
Gewicht:
688 g
Format:
241x160x25 mm
Sprache:
Englisch
Beschreibung:
This monograph offers an introduction to finite Blaschke products and their connections to complex analysis, linear algebra, operator theory, matrix analysis, and other fields. Old favorites such as the Carathéodory approximation and the Pick interpolation theorems are featured, as are many topics that have never received a modern treatment, such as the Bohr radius and Ritt's theorem on decomposability. Deep connections to hyperbolic geometry are explored, as are the mapping properties, zeros, residues, and critical points of finite Blaschke products. In addition, model spaces, rational functions with real boundary values, spectral mapping properties of the numerical range, and the Darlington synthesis problem from electrical engineering are also covered.
Explains connections in complex analysis, linear algebra, operator theory, and electrical engineering
Preface.- Notations.- 1. Geometry of the Schur class.- 2. Elementary hyperbolic geometry.- 3. Finite Blaschke products: the basics.- 4. Approximation by finite Blaschke products.- 5. Zeros and residues.- 6. Critical points.- 7. Interpolation.- 8. The Bohr radius.- 9. Finite Blaschke products and group theory.- 10. Finite Blaschke products and operator theory.- 11. Real complex functions.- 12. Finite-dimensional model spaces.- 13. The Darlington synthesis problem.- A. Some reminders.- Index.
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