Interpolation Theory and Its Applications

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Focusing on operator identities, this book explores interpolation problems, highlighting their significance in both theory and application. It presents a general framework that encompasses classical issues like Nevanlinna Pick and Caratheodory, while deriving the Potapov inequality and detailing its solutions through linear-fractional transformations. The text further extends these findings to various classical and contemporary problems, including extension problems, spectral theory, and nonlinear integrable equations, showcasing the versatility of interpolation theory.