Finite Blaschke Products and Their Connections

Focusing on finite Blaschke products, this monograph delves into their relevance across multiple disciplines, including complex analysis and operator theory. It revisits classic theorems like Carathéodory approximation and Pick interpolation while introducing modern treatments of topics such as the Bohr radius and Ritt's theorem. The text explores connections to hyperbolic geometry, mapping properties, and critical points, alongside discussions on model spaces, spectral mapping, and applications in electrical engineering, notably the Darlington synthesis problem.