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.

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E-mail: chairman.math[at]iisc[dot]ac[dot]in