Second Level Degree in Mathematics
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FUNCTIONS OF SEVERAL COMPLEX VARIABLES - 6 CFU
Teacher
Luca Baracco
Scheduled Period
I Year - 1 Semester | 30/09/2019 - 18/01/2020
Hours: 48 (24 esercitazione, 24 lezione)
Prerequisites
Integral and differential calculus in several variables.
Target skills and knowledge
Knowledge of the basic properties of holomorphic functions in several variables. In particular learning the techniques for dealing with such functions.
Examination methods
Oral exam
Assessment criteria
Knowledge of the topics exposed in class.
Course contents
1. Real and complex differentials
2. Cauchy formula on polydiscs
3. Subharmonic functions
4. Separate analytic functions
5. Analytic functions and convergent power series
6. Levi form and H. Lewy's extension theorem
7. Logarithmic Superharmonicity, Continuity principle, Propagation of holomorphic extendibility
8. Domains of holomorphy end pseudoconvex domains
9. L2 estimates and Neumann problem
Planned learning activities and teaching methods
lectures and tutorials