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Schwarzian derivative

Definition

The Schwarzian derivative is an operator on complex functions that is invariant under fractional linear transformations:

(Sf)(z):=(f(z)f(z)) 12(f(z)f(z)) 2=f(z)f(z)32(f(z)f(z)) 2 (S f)(z) := \left( \frac{f''(z)}{f'(z)}\right)^' - \, \frac{1}{2} \left( \frac{f''(z)}{f'(z)}\right)^2 = \frac{f'''(z)}{f'(z)} - \frac{3}{2}\left( \frac{f''(z)}{f'(z)}\right)^2

In fact the Schwarzian derivative of a fractional linear transformation, considered as a function from \mathbb{C} to \mathbb{C}, is zero.

References

category: analysis

Last revised on November 12, 2018 at 08:46:56. See the history of this page for a list of all contributions to it.