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

Leah K. Mork, Keith Sullivan and Darin J. Ulness
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Leah K. Mork: Department of Mathematics, Concordia College, Moorhead, MN 56562, USA
Keith Sullivan: Department of Mathematics, Concordia College, Moorhead, MN 56562, USA
Darin J. Ulness: Department of Chemistry, Concordia College, Moorhead, MN 56562, USA

Mathematics, 2020, vol. 8, issue 4, 1-17

Abstract: 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.

Keywords: lacunary function; gap function; centered polygonal numbers; natural boundary; singularities; broom topology (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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