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Complex analysis.

Look up **
complex analysis** in Wiktionary, the free dictionary.

**
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.

- Complex analysts (85 P)
- Complex dynamics (15 P)
- Conformal mappings (19 P)

- Hardy spaces (9 P)

The following 126 pages are in this category, out of 126 total. This list may not reflect recent changes.

- Calderón projector
- Cartan's lemma (potential theory)
- Cauchy product
- Cauchy–Riemann equations
- Complex convexity
- 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