High Quality Content by WIKIPEDIA articles! This is an easy consequence of the Schwarz–Pick theorem mentioned above: One just needs to remember that the Cayley transform W(z) = (z – i)/(z + i) maps the upper half-plane H conformally onto the unit disc D. Then, the map W o o W–1 is a holomorphic map from D onto D. Using the Schwarz–Pick theorem on this map, and finally simplifying the results by using the formula for W, we get the desired result. Also, for all z H, frac{left|f'(z)right|}{mbox{Im }f(z)} le frac{1}{mbox{Im }(z)}.

Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.