250112 VO Selected topics in complex analysis (2013S)

Steven Krantz writes in the introduction to
his book: "One might be tempted to think of the analysis of several complex variables as being esentially one variable theory with additional complication of multi-indices. This perception turns out to be incorrect. Deep new phenomena and profound problems present themselves in the theory of several variables." We start with a comparison of the theory in one complex variable and in several variables. The essential differences are used as a motivation and guideline for the lecture course. Holomorphic functions, power series, Cauchy-Riemann differential equations, domains of holomorphy, pseudoconvex domains, Hörmander's L^2
estimates for the solution of the inhomogeneous Cauchy-Riemann differential equations.