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Qualifying Exam

Date:
-
Location:
341 White Hall Classroom Bulding
Speaker(s) / Presenter(s):
Stephen Deterding, University of Kentucky

Title:  On Bounded Point Derivations and Analytic Capacity

Abstract:  Let X be a compact subset of the complex plane and let R(X) denote the uniform closure of the space of rational functions whose poles lie off X. We say that there is a bounded point derivation on R(X) at x if and only if there exists a constant k such that |f t(x)| ≤ k||f ||X for all f ∈ H(X), where H(X) is the space of all functions that are holomorphic in some neighborhood of X. In this talk we will give necessary and sufficient conditions for the existence of a bounded point derivation on R(X) at x.
 

 

 

 

 

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