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 fi rst part ends
with an analytic characterization of simply connected domains. The
second part is concerned with functional analytic methods: Frechet
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. Contents Complex numbers
and functions Cauchy's Theorem and Cauchy's formula Analytic
continuation Construction and approximation of holomorphic
functions Harmonic functions Several complex variables Bergman
spaces The canonical solution operator to Nuclear Frechet spaces of
holomorphic functions The -complex The twisted -complex and
Schroedinger operators
General
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