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| + | This is in regards to Homework 3 Problem 4. In order to show that <math>{f}</math> is constant on <math>\Omega</math> I let <math>\gamma</math> be a closed circle in <math>\Omega</math>. Knowing that <math>{f}</math> is analytic on <math>\Omega</math> we know the integral over <math>\gamma</math> is zero. Letting <math>\omega\in\gamma</math> we can set <math>f(\omega)=z\in\Gamma</math>. My question is based on <math>\rho</math> and what we know about it and how it relates to <math>\Gamma</math> what can we know about <math>f(\gamma)</math>? I think this will help as far as proving f is constant. | ||
Latest revision as of 11:44, 8 February 2010
Homework 3
This is in regards to Homework 3 Problem 4. In order to show that $ {f} $ is constant on $ \Omega $ I let $ \gamma $ be a closed circle in $ \Omega $. Knowing that $ {f} $ is analytic on $ \Omega $ we know the integral over $ \gamma $ is zero. Letting $ \omega\in\gamma $ we can set $ f(\omega)=z\in\Gamma $. My question is based on $ \rho $ and what we know about it and how it relates to $ \Gamma $ what can we know about $ f(\gamma) $? I think this will help as far as proving f is constant.
