Cayley transform between the half-plane and disk
= Cayley transform between the half-plane and disk
The fractional linear maps
$$
w=\frac{z-1}{z+1},
\qquad
z=\frac{1+w}{1-w}
$$
map the right half-plane and unit disk conformally onto one another.
= Cayley transform between the half-plane and disk
The fractional linear maps
$$
w=\frac{z-1}{z+1},
\qquad
z=\frac{1+w}{1-w}
$$
map the right half-plane and unit disk conformally onto one another.