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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)

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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

Additional notes about suggested reading

Textbooks (and optional supplementary readings)

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