Explore the cutting-edge theory of functions of a-bounded type in the half-plane with this essential volume from “The bookish owl.” Leveraging Liouville integro-differentiation, this work builds upon M.M. Djrbashian’s factorization theory, drawing parallels between disc and half-plane function classes. Discover significant improvements to the Phragmen-Lindelöf Principle and Nevanlinna Factorization in the Half-Plane. This book introduces an innovative, equivalent definition for classical Hardy spaces and presents a novel application in spectral theory for linear operators, a problem long posed by M.G. Krein. Ideal for graduate students, young researchers, and specialists in complex analysis and operator theory.