Functions with No Unbounded Fatou Components
Ramanpreet Kaur
TL;DR
This paper investigates the properties of transcendental entire functions, providing partial answers to longstanding questions about the boundedness of their Fatou components and addressing related questions on Fejér gaps.
Contribution
It offers new insights into the boundedness of Fatou components for certain transcendental entire functions and generalizes results on functions with Fabry gaps and infinite order.
Findings
Partial affirmative answer to Baker's question on bounded Fatou components
Addressed Wang's question on Fejér gaps
Generalized results for functions with Fabry gaps and infinite order
Abstract
For a transcendental entire function, a partial affirmative answer to Baker's question on the boundedness of its Fatou components is given. In addition, we have addressed Wang's question on Fej\'er gaps. Certain results about functions with Fabry gaps and of infinite order have also been generalized.
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Taxonomy
TopicsMeromorphic and Entire Functions · Functional Equations Stability Results · Mathematics and Applications