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Open AccessArticle

Taming the Natural Boundary of Centered Polygonal Lacunary Functions—Restriction to the Symmetry Angle Space

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Department of Mathematics, Concordia College, Moorhead, MN 56562, USA
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Department of Chemistry, Concordia College, Moorhead, MN 56562, USA
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 568; https://doi.org/10.3390/math8040568
Received: 16 March 2020 / Revised: 3 April 2020 / Accepted: 6 April 2020 / Published: 11 April 2020
(This article belongs to the Special Issue Geometrical Theory of Analytic Functions)
This work investigates centered polygonal lacunary functions restricted from the unit disk onto symmetry angle space which is defined by the symmetry angles of a given centered polygonal lacunary function. This restriction allows for one to consider only the p-sequences of the centered polygonal lacunary functions which are bounded, but not convergent, at the natural boundary. The periodicity of the p-sequences naturally gives rise to a convergent subsequence, which can be used as a grounds for decomposition of the restricted centered polygonal lacunary functions. A mapping of the unit disk to the sphere allows for the study of the line integrals of restricted centered polygonal that includes analytic progress towards closed form representations. Obvious closures of the domain obtained from the spherical map lead to four distinct topological spaces of the “broom topology” type. View Full-Text
Keywords: lacunary function; gap function; centered polygonal numbers; natural boundary; singularities; broom topology lacunary function; gap function; centered polygonal numbers; natural boundary; singularities; broom topology
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Mork, L.K.; Sullivan, K.; Ulness, D.J. Taming the Natural Boundary of Centered Polygonal Lacunary Functions—Restriction to the Symmetry Angle Space. Mathematics 2020, 8, 568.

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