Blaschke product estimates

April 7, 2009

Here’s something that should be in every complex analysis text, but aparently isn’t. But it’s here on my blog, so never fear!

You know the boundary values of a holomorphic function f on the disc, and you know one of its values on the interior. How many zeroes can there be? And how tightly can you quarantine away the set where |f| is small? Blaschke products, Harnack’s inequality, and the maximum modulus principle used together provide one partial answer.

Click here for the short paper.

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