Ondrej Kalenda

Complex Analysis 2

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Organization of the course

Content of the course, expected knowledge and connections to other courses

Recommended literature

Lecture notes

Information on classes and course credit

Program jednotlivých přednášek a cvičení

Informace ke zkouškám

Content of the course, expected knowledge and connections to other courses

The aim of this course is to provide an introduction to several advanced areas of complex analysis. Main topics are the following:

1. Harmonic functions of two variables and their relationship to holomorphic functions (boundary behavior of harmonic and holomorphic functions)
2. Analytic continuation (continuation along a curve, analytic multifunctions, few facts on Rieman surfaces)
3. Functions of several complex variables (convergence of power series of several variables, domains of holomorphy, Hartogs extension theorem, Hartogs theorem on separate holomorphy)

Complex analysis 2 is an advanced course for master students of mathematical analysis. Therefore the knowledge on the level of the bachelor program General mathematics, specialization Mathematical analysis os expected.

More specifically, this course is a kind of continuation of the bachelor course Complex Analysis 1 (NMMA338) which itself is a continuation of the course Introduction to complex analysis (NMMA301). Besides, we will need a sound knowledge of measure and integration and several things from functional analysis.

How to continue?

Some topics related to the first chapter are studied in the optional courses Introduction to Harmonic Analysis 1, 2 (NMMA477, NMMA478), Advanced Differentiation and Integration 4 (NMMA564), Quasi-Conformal Mappings 1, 2 (NMMA577, NMMA578). A kind of continuation of the second chapter is in the elective course Riemann surfaces (NMAG433). A further optional course devoted to topics related to complex analysis is Hypercomplex Analysis (NMAG461).