meromorphic functions of several variables
Note that is really defined only outside of a complex analytic subvariety. Unlike in one variable, we cannot simply define to be equal to at the poles and expect to be a continuous mapping to some larger space (the Riemann sphere in the case of one variable). The simplest counterexample in is , which does not have a unique limit at the origin. The set of points where there is no unique limit, is called the indeterminancy set. That is, the set of points where if , and and have no common factors, then the indeterminancy set of is the set where .
- 1 Lars Hörmander. , North-Holland Publishing Company, New York, New York, 1973.
- 2 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
|Title||meromorphic functions of several variables|
|Date of creation||2013-03-22 16:01:10|
|Last modified on||2013-03-22 16:01:10|
|Last modified by||jirka (4157)|