Finite Blaschke Products and Their Connections

Stephan Ramon Garcia is a professor of mathematics at Pomona CollegeJavad Mashreghi is a professor in the Department of Mathematics and Statistics at Laval University, Alexandre-Vachon. William T. Ross is a professor of mathematics and the Chair of the Department of Math and Computer Sciences at the University of Richmond.

• 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.

“The book under consideration is concerned with finite Blaschke products. … The book is designed for students and researchers familiar with basic real and complex analysis and linear algebra. The proofs are detailed and dozens illustrations are provided. At the end of each chapter, the authors include exercises so that the reader can gain greater technical fluency with the material and appreciate the beauty of the subject.” (Leonid Golinskii, zbMATH 1398.30002, 2018)