Several Complex Variables
- Lecture notes (as of November 30)
- Course description
- This course is an introduction to the theory of functions of
several complex variables. The emphasis is on the part of the
theory that intersects with analysis and with partial differential
Here are some of the topics that will be discussed (although not
in linear order).
- Multi-variable power series
- Reinhardt domains
- domains of convergence
- the Hartogs phenomenon
- entire functions
- Integral representations
- Cauchy integral
- Bochner–Martinelli integral
- Bergman kernel function
- Notions of convexity
- linear convexity
- polynomial convexity
- holomorphic convexity
- Levi problem
- d-bar problem
- Holomorphic mappings
- You should have some acquaintance at the first-year graduate
level with both real analysis and (one-variable) complex analysis.
The official prerequisites for this course are Math 608 and
- The course meets 11:10–12:25 on Tuesday and Thursday in
room 624 of the Blocker building.
- Course website
- There is no required textbook. I have asked the library to put
the following books on reserve.
- Lars Hörmander, An introduction to complex analysis in
several variables, second edition, North-Holland, 1973;
QA331 .H64 1973.
- Steven G. Krantz, Function theory of several complex
variables, second edition, American Mathematical Society,
2001; QA331.7 .K74 2001.
- R. Michael Range, Holomorphic functions and integral
representations in several complex variables, Springer-Verlag,
1986; QA331 .R355 1986.
- Volker Scheidemann, Introduction to complex analysis in
several variables, Birkhäuser, 2005; QA331.7 .S34 2005.
- Grades will be based on class participation and homework.
- Office hours
During the Fall 2011 semester, my office hour in Milner 202 is 2:00–3:00 in the afternoon on Monday and Wednesday; I am available also by appointment. The best way to contact me is via email to firstname.lastname@example.org. Telephone messages can be left at the Milner office of the Department of Mathematics, 979-845-7554.
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