Complex Analysis: A Functional Analytic Approach

"In this textbook, a concise approach to complex analysis of one and several variables is presented. After an introduction of Cauchy's integral theorem general versions of Runge's approximation theorem and Mittag-Leffler's theorem are discussed. The first part ends with an analytic characterization of simply connected domains. The second part is concerned with functional analytic methods: Fréchet and Hilbert spaces of holomorphic functions, the Bergman kernel, and unbounded operators on Hilbert spaces to tackle the theory of several variables, in particular the inhomogeneous Cauchy-Riemann equations and the d-bar Neumann operator. [It serves as:] a modern approach to complex analysis of one and several variables; covers several variables using methods of functional analysis; well suited for introductory and advanced courses on complex analysis; [and] includes many exercises related to the content of each chapter." -- rear cover.