Interpolation Theory and Its Applications

Focusing on interpolation problems, the book employs operator identities to explore both classical and contemporary issues in this field. It presents a general framework that encompasses well-known interpolation problems such as Nevanlinna Pick and Schur, and formulates the abstract Potapov inequality. The solutions are expressed through linear-fractional transformations. Additionally, the text applies these findings to various other domains, including extension problems, generalized stationary processes, and spectral theory, showcasing the versatility of interpolation theory.