T-universal Functions With Prescribed Approximation Curves

Details T-universal Functions With Prescribed Approximation Curves T-universal Functions With Prescribed Approximation Curves

2003-11-13

arxiv.org/abs/math/0311229v1

Mathematics

Complex Variables

References corrected

Scientific paper

Let be F a family of curves in the unit disc. We show that the set of all functions f holomorphic on the unit disc, which satisfy the following condition, is G-delta and dense in the space of all functions holomorphic on the unit disc: For each compact set K with connected complement, each function g continuous on K and holomorphic on its interior, every point t on the unit circle, every curve C in F (ending in t) and any e>0 there exist numbers 0

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