### MA 328: Introduction to Several Complex Variables

#### Credits: 3:0

Preliminaries: Holomorphic functions in $C^n$ : definition , the generalized Cauchy integral formula, holomorphic functions: power series development(s), circular and Reinhardt domains, analytic continuation : basic theory and comparisons with the one- variable theory.

Convexity theory: Analytic continuation: the role of convexity, holomorphic convexity, plurisub-harmonic functions, the Levi problem and the role of the d-bar equation.

The d- bar equation: Review of distribution theory, Hormander’s solution and estimates for the d-bar operator.

#### Suggested books :

1. Lars Hormander, An Introduction to Complex Analysis in Several Variables, 3rd edition ,North-Holland Mathematical Library, North-Holland, 1989.
2. Function Theory of Several Complex Variables, 2nd edition ,Wadsworth & Brooks/Cole, 1992.
3. Raghavan Narasimhan, Several Complex Variables ,Chicago Lectures in Mathematics Series, The University of Chicago Press, 1971.

#### All Courses

Contact: +91 (80) 2293 2711, +91 (80) 2293 2625
E-mail: chairman.math[at]iisc[dot]ac[dot]in