Valid from: Spring 2019
Decided by: Professor Thomas Johansson
Date of establishment: 2019-09-12
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: MATP22
Teaching language: English
The aim of the course is to give an overview of the field of complex analysis in several variables, in particular hightlighting the differences from and the similarities with complex analysis in one variable,
Knowledge and Understanding
For a passing grade the doctoral student must
Basic properties of holomorphic functions. Analytic continuation and power series in several variables. The inhomogeneous Cauchy-Riemann equation. The Weierstrass preparation theorem, zero sets and singularities. Hartog's theorem. Holomorphic mappings and complex manifolds. Convexity and holomorphic convexity. Domains of holomorphy. The first Cousin problem. The Levi problem. Pluripotential theory. Pseudoconvex domains. Integral representation formulas. Solutions of the d-bar equation for pseudoconvex domains.
Korevaar, J. & Wiegerinck, J.: Lecture notes in several complex variables. 2017.
Freely available from https://staff.science.uva.nl/j.j.o.o.wiegerinck/edu/scv/scvboek.pdf
Type of instruction: Lectures
Examination format: Oral exam
Grading scale: Failed, pass
Assumed prior knowledge: Complex analysis in one variable, Fourier analysis and Functional Analysis.
Web page: http://www.maths.lth.se/matematiklth/personal/frankw/#/scv19