

Several Complex Variables
פונקציות מרוכבות במספר משתנים
Fall semester, October 2009  January 2010
Lecturer
Bo'az Klartag
Room 229, Schreiber building
Phone: 036406957
Email:
Classes
Tuesday, 1618, Kaplun 319
Wednesday 1617, Shenkar 1314
Final grade
There will be 35 home assignments throughout the semester.
Recommended literature All of the following books are available at the library:
 L. Hormander, An introduction to complex analysis in several variables (we will cover chapters 1,2 and 4).
 B. Shabat, An introduction to complex analysis, part II (translation from Russian).
 S. Krantz, Function theory of several complex variables (more detailed).
 R. Narasimhan, Several Complex Variables.
 M. Herve, Several Complex Variables.
Syllabus
Functions in several complex variables, pluriharmonic functions,
holomorphic and biholomorphic mappings.
The phenomenon of forced analytic continuation, Hartogs extension
theorem, Reinhardt domains. Domains of holomorphy, dbar equation.
Subharmonic and plurisubharmonic functions, pseudoconvex sets,
analogy with realvariable convexity.
Existence theorems for dbar equation, Levi's problem.
PrekopaLeindler and Berdntsson's inequalities, applications to
convex geometry.
Exercises
Exercise 1
Exercise 2
Exercise 3
Exercise 4
The grades of the exercises.
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