Complex analysis problem regarding the maximum principle

Hi,

I have a problem in comple analysis which regards the maximum principle that I would love to get some help with. The question is :

Let g be an analytic function in a ring S = {z | a < |Z|< b }which is continuous on the circle {z | |z| = b}. Also f(z) = 0 for every z on that circle.

Prove that f(z) = 0 for every z in S.

As I mentioned above it has to do with the maximum principle.

Looking forward for your help, anyone.

Thanks.

Popo

will anybody help me please ?

I've posted this question more than one week with no reply since.

Will anybody please help/ give an idea ?

Thanks !