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Complex analysis is the branch of mathematics investigating holomorphic functions, i.e. functions which are defined in some region of the complex plane, take complex values, and are differentiable as complex functions. Complex differentiability has much stronger consequences than usual (real) differentiability. For instance, every holomorphic function is representable as power series in every open disc in its domain of definition, and is therefore analytic. In particular, holomorphic functions are infinitely differentiable, a fact that is far from true for real differentiable functions. Most elementary functions, such as all polynomials, the exponential function, and the trigonometric functions, are holomorphic. See also : holomorphic sheaves and vector bundles.
This category has the following 15 subcategories, out of 15 total.
- Hardy spaces (9 P)
- Potential theory (3 C, 36 P)
Pages in category "Complex analysis"
The following 125 pages are in this category, out of 125 total. This list may not reflect recent changes ( learn more).
- Calderón projector
- Cartan's lemma (potential theory)
- Cauchy product
- Cauchy–Riemann equations
- Complex convexity
- Complex differential equation
- Complex line
- Complex plane
- Complex polytope
- Conformal radius
- Conformal welding
- Connectedness locus
- Continuous functions on a compact Hausdorff space
- A Course of Modern Analysis
- Cousin problems