Math 650-600
Several Complex Variables

Harold P. Boas

Fall 2007

The course

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 equations.

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
  • pseudoconvexity
• Levi problem
• d-bar problem
• Holomorphic mappings

Prerequisites

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 Math 618.

Venue

The course meets 9:10-10:00 on Monday, Wednesday, and Friday in HALB 104.

Web site

The course web site is /~boas/courses/650-2007c/

Textbook

There is no required textbook. I have asked the library to put the following books on reserve with a three-day checkout period.

• Klaus Fritzsche and Hans Grauert, From holomorphic functions to complex manifolds, Springer, 2002; QA331.7 .F75 2002.
• 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.
• Raghavan Narasimhan, Several complex variables, University of Chicago Press, 1971; QA331 .N29.
• R. Michael Range, Holomorphic functions and integral representations in several complex variables, Springer-Verlag, 1986; QA331 .R355 1986.

Grading

Grades will be based on class participation.

The instructor

The instructor is Dr. Harold P. Boas. Office hours are in 202 Milner Hall, 11:00-12:00 on Monday, Wednesday, and Friday; also by appointment. The office telephone number is (979) 845-7269, and the email address is boas@tamu.edu.

Other information

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