Friedrich Haslinger: Complex Analysis, Kartoniert / Broschiert

Klappentext

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: 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.
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 Fréchet spaces of holomorphic functions
The -complex
The twisted -complex and Schrödinger operators