The transformation of all complex numbers on the unit circle is a special case.

Thus the complex unit circle maps to a flat plate on the real number line from 2 to +2.

The region of convergence must therefore include the unit circle.

In fact we see that the image of h is the unit circle.

If it so happens that then the point is within the unit circle and should be accepted.

Let us go back to the example of the unit circle.

This means the unit circle must be the continuous spectrum of "T".

See the unit circle at the left of Figure 2.

Another simple example is the unit circle, S (see picture above).

Also note that if we consider this as a function from the unit circle to the real numbers, then it is neither open nor closed.