Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 739–749

IDENTIFYING LOGARITHMIC TRACTS

James Waterman

The Open University, School of Mathematics and Statistics
Walton Hall, Milton Keynes MK7 6AA, United Kingdom; james.waterman 'at' open.ac.uk

Abstract. We show that a direct tract bounded by a simple curve is a logarithmic tract and further give sufficient conditions for a direct tract to contain logarithmic tracts. As an application of these results, it is shown that an example of a function with infinitely many direct singularities, but no logarithmic singularity over any finite value, is in the Eremenko–Lyubich class.

2010 Mathematics Subject Classification: Primary 30D05; Secondary 37F10.

Key words: Logarithmic tracts, transcendental entire functions, harmonic functions.

Reference to this article: J. Waterman: Identifying logarithmic tracts. Ann. Acad. Sci. Fenn. Math. 45 (2020), 739–749.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4543