Several complex variables (nonfiction): Difference between revisions
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The theory of functions of '''several complex variables''' is the branch of mathematics dealing with complex valued functions | The theory of functions of '''several complex variables''' is the branch of mathematics dealing with complex valued functions on the space Cn of n-tuples of [[Complex number (nonfiction)|complex numbers]]. | ||
As in [[Complex analysis (nonfiction)|complex analysis]], which is the case n = 1 but of a distinct character, these are not just any functions: they are supposed to be holomorphic or complex analytic, so that locally speaking they are power series in the variables zi. | |||
Equivalently, as it turns out, they are locally uniform limits of polynomials; or local solutions to the n-dimensional Cauchy–Riemann equations. | Equivalently, as it turns out, they are locally uniform limits of polynomials; or local solutions to the n-dimensional Cauchy–Riemann equations. | ||
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== Nonfiction cross-reference == | == Nonfiction cross-reference == | ||
* [[Complex analysis (nonfiction)]] | |||
* [[Complex number (nonfiction) | * [[Complex number (nonfiction) | ||
* [[Mathematics (nonfiction)]] | * [[Mathematics (nonfiction)]] | ||
Revision as of 08:15, 19 August 2018
The theory of functions of several complex variables is the branch of mathematics dealing with complex valued functions on the space Cn of n-tuples of complex numbers.
As in complex analysis, which is the case n = 1 but of a distinct character, these are not just any functions: they are supposed to be holomorphic or complex analytic, so that locally speaking they are power series in the variables zi.
Equivalently, as it turns out, they are locally uniform limits of polynomials; or local solutions to the n-dimensional Cauchy–Riemann equations.
In the News
Fiction cross-reference
Nonfiction cross-reference
- Complex analysis (nonfiction)
- [[Complex number (nonfiction)
- Mathematics (nonfiction)
External links:
- Several complex variables @ Wikipedia