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Uniform Approximation On Riemann Surfaces, Fatemeh Sharifi
Uniform Approximation On Riemann Surfaces, Fatemeh Sharifi
Electronic Thesis and Dissertation Repository
This thesis consists of three contributions to the theory of complex approximation on
Riemann surfaces. It is known that if E is a closed subset of an open Riemann surface R and f is a holomorphic function on a neighbourhood of E, then it is usually not possible to approximate f uniformly by functions holomorphic on all of R. Firstly, we show, however, that for every open Riemann surface R and every closed subset E of R; there is closed subset F of E, which approximates E extremely well, such that every function holomorphic on F can be approximated much …