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A note on regularly asymptotic points

Jiří Jelínek (1996)

Commentationes Mathematicae Universitatis Carolinae

A condition of Schmets and Valdivia for a boundary point of a domain in the complex plane to be regularly asymptotic is ameliorated.

A note on the three-segment problem

Martin Doležal (2009)

Mathematica Bohemica

We improve a theorem of C. L. Belna (1972) which concerns boundary behaviour of complex-valued functions in the open upper half-plane and gives a partial answer to the (still open) three-segment problem.

Asymptotic values and the growth of analytic functions in spiral domains.

James E. Brennan, Alexander L. Volberg (1993)

Publicacions Matemàtiques

In this note we present a simple proof of a theorem of Hornblower which characterizes those functions analytic in the open unit disk having asymptotic values at a dense set in the boundary. Our method is based on a kind of ∂-mollification and may be of use in other problems as well.

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