Strongly Annular Fungi-ions with Small Coefficients, and Related Results

Abstract

for some sequence of Jordan curves J, in D with 0 in their interiors. An example of an annular function for which (0.2) holds was known previously 14, p. lool. 12, p. 21 I. While it is known that not every annular function is strongly annular 131, one might speculate that cvcry annular function enjoys some of the special properties of the strongly annular functions. For example, given an annular function ,f. can the {J,,) satisfying (0.4) always be chosen so that the sequence of lengths I (J,) remains hounded’! Can the (J,,) be chosen so that the ratio of the distances to IzI = I from the closest and Furthest points of J,, is bounded away from zero as n increiiscs? In $2, WC construct a countercxamplc to these conjeclures. Both constructions make use of a technique of Bagemihl and Seidel [l, pp. 188 1901.

Cite this paper

@inproceedings{Bonar2001StronglyAF, title={Strongly Annular Fungi-ions with Small Coefficients, and Related Results}, author={David Bonar}, year={2001} }