Exponential taylor domination

Omer Friedland*, Gil Goldman, Yosef Yomdin

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


Let (Equation presented) be an analytic function in a disk DR of radius R > 0, and assume that f is p-valent in DR, i.e. it takes each value c∈C at most p times in DR. We consider its Borel transform (Equation presented) which is an entire function, and show that, for any R > 1, the valency of the Borel transform B(f) in DR is bounded in terms of p, R. We give examples, showing that our bounds, provide a reasonable envelope for the expected behavior of the valency of B(f). These examples also suggest some natural questions, whose expected answer will strongly sharper our estimates. We present a short overview of some basic results on multi-valent functions, in connection with “Taylor domination”, which, for (Equation presented), is a bound of all its Taylor coefficients ak through the first few of them. Taylor domination is our main technical tool, so we also discuss shortly some recent results in this direction.

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages10
StatePublished - 2020
Externally publishedYes

Publication series

NameOperator Theory: Advances and Applications
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878


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