Finite Blaschke Products and Their Connections

• Main Authors: Garcia, Stephan Ramon (Author, http://id.loc.gov/vocabulary/relators/aut), Mashreghi, Javad (http://id.loc.gov/vocabulary/relators/aut), Ross, William T. (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Subjects: Functional analysis.; Operator theory.; Functional Analysis.; Operator Theory.

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...

Table of Contents:

• 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.