Taming the Natural Boundary of Centered Polygonal Lacunary Functions—Restriction to the Symmetry Angle Space
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 <i>p</i>-sequences of the cen...
Main Authors: | , , |
---|---|
Format: | Article |
Language: | English |
Published: |
MDPI AG
2020-04-01
|
Series: | Mathematics |
Subjects: | |
Online Access: | https://www.mdpi.com/2227-7390/8/4/568 |
_version_ | 1797570813951475712 |
---|---|
author | Leah K. Mork Keith Sullivan Darin J. Ulness |
author_facet | Leah K. Mork Keith Sullivan Darin J. Ulness |
author_sort | Leah K. Mork |
collection | DOAJ |
description | 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 <i>p</i>-sequences of the centered polygonal lacunary functions which are bounded, but not convergent, at the natural boundary. The periodicity of the <i>p</i>-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. |
first_indexed | 2024-03-10T20:30:44Z |
format | Article |
id | doaj.art-286452890a314b899794b7e3903ec61b |
institution | Directory Open Access Journal |
issn | 2227-7390 |
language | English |
last_indexed | 2024-03-10T20:30:44Z |
publishDate | 2020-04-01 |
publisher | MDPI AG |
record_format | Article |
series | Mathematics |
spelling | doaj.art-286452890a314b899794b7e3903ec61b2023-11-19T21:22:45ZengMDPI AGMathematics2227-73902020-04-018456810.3390/math8040568Taming the Natural Boundary of Centered Polygonal Lacunary Functions—Restriction to the Symmetry Angle SpaceLeah K. Mork0Keith Sullivan1Darin J. Ulness2Department of Mathematics, Concordia College, Moorhead, MN 56562, USADepartment of Mathematics, Concordia College, Moorhead, MN 56562, USADepartment of Chemistry, Concordia College, Moorhead, MN 56562, USAThis 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 <i>p</i>-sequences of the centered polygonal lacunary functions which are bounded, but not convergent, at the natural boundary. The periodicity of the <i>p</i>-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.https://www.mdpi.com/2227-7390/8/4/568lacunary functiongap functioncentered polygonal numbersnatural boundarysingularitiesbroom topology |
spellingShingle | Leah K. Mork Keith Sullivan Darin J. Ulness Taming the Natural Boundary of Centered Polygonal Lacunary Functions—Restriction to the Symmetry Angle Space Mathematics lacunary function gap function centered polygonal numbers natural boundary singularities broom topology |
title | Taming the Natural Boundary of Centered Polygonal Lacunary Functions—Restriction to the Symmetry Angle Space |
title_full | Taming the Natural Boundary of Centered Polygonal Lacunary Functions—Restriction to the Symmetry Angle Space |
title_fullStr | Taming the Natural Boundary of Centered Polygonal Lacunary Functions—Restriction to the Symmetry Angle Space |
title_full_unstemmed | Taming the Natural Boundary of Centered Polygonal Lacunary Functions—Restriction to the Symmetry Angle Space |
title_short | Taming the Natural Boundary of Centered Polygonal Lacunary Functions—Restriction to the Symmetry Angle Space |
title_sort | taming the natural boundary of centered polygonal lacunary functions restriction to the symmetry angle space |
topic | lacunary function gap function centered polygonal numbers natural boundary singularities broom topology |
url | https://www.mdpi.com/2227-7390/8/4/568 |
work_keys_str_mv | AT leahkmork tamingthenaturalboundaryofcenteredpolygonallacunaryfunctionsrestrictiontothesymmetryanglespace AT keithsullivan tamingthenaturalboundaryofcenteredpolygonallacunaryfunctionsrestrictiontothesymmetryanglespace AT darinjulness tamingthenaturalboundaryofcenteredpolygonallacunaryfunctionsrestrictiontothesymmetryanglespace |