Faculty of Mathematics and Physics

Lecture notes to the course Complex Analysis 2

Summer semester 2018/2019

Lecture notes to the preceeding courses (only in Czech)

Complex Analysis 1 (2017/2018)

Introduction Complex Analysis (2017/2018)

During the lectures some results from student's presentations from Complex Analysis 1 are used. They are collected here.

IX. Harmonic functions of two variables

IX.1 Harmonic and holomorphic functions -

IX.2 Boundary behavior of holomorphic functions -

        Důkaz Věty IX.10 a jejích důsledků

        Důkaz Lemmatu IX.11

        Důkaz Věty IX.12 a jejího důsledku

IX.3 Hardy spaces on the unit disc -

        Důkaz Věty IX.18

        Důkaz Věty IX.19 a jejího důsledku

        Důkaz Věty IX.20

        Důkaz Věty IX.21

X. Analytic continuation

X.1 Function elements and their continuation -

X.2 Multifunctions admitting unrestricted continuation -

X.3 Few facts on Riemann surfaces -

XI. Introduction to holomorphic functions of several variables

XI.1 Power series of several complex variables -

        Důkaz Věty XI.4

XI.2 Holomorphic functions of several variables -

XI.3 Hartogs extension thm., domains of holomorphy -

        Důkaz Věty XI.13

        Důkaz Věty XI.14 (a jejího důsledku)

XI.4 Hartogs theorem on separate holomorphy -

        Důkaz Lemmat XI.16 a XI.17

        Důkaz Lemmatu XI.18 a Věty XI.15