Syllabus
1. Harmonic funcrtions of two variables (relationship of harmonic and holomorphic functions, Poisson integral, Schwarz relfection principle, boundary behaviour of harmonic and holomorphic functions, Hardy spaces on the disc) 2. Analytic functions (basic properties, monodromy theorem, Riemannian manifolds, singularities of analytic functions). 3.
Functions of several complex variables (domains of convergence of power series, Hartogs' paradox and Hartogs' theorem).
Annotation
Mandatory course for the master study branch Mathematical analysis. Recommended for the first year of master studies.
Introduction to advanced topics in complex analysis - harmonic functions of two real variables and their relationship to holomorphic functions, boundary behaviour of holomorphic functions, analytic continuation, elements of the theory of functions of several complex variables.
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