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Extending the Geometric Modulus Principle.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Extending the Geometric Modulus Principle./
Author:	Hohertz, Matthew Ryan.
Description:	1 online resource (54 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 83-08, Section: B.
Contained By:	Dissertations Abstracts International83-08B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28962805click for full text (PQDT)
ISBN:	9798790631139

Extending the Geometric Modulus Principle.
Hohertz, Matthew Ryan.

Extending the Geometric Modulus Principle. - 1 online resource (54 pages)

Source: Dissertations Abstracts International, Volume: 83-08, Section: B.

Thesis (Ph.D.)--Rutgers The State University of New Jersey, School of Graduate Studies, 2022.

Includes bibliographical references

In a 2011 paper, Kalantari observes that complex polynomials exhibit a certain symmetry with respect to argument at every point. To wit, if the polynomial $p(z)$ has order $k$ as an analytic function whose germ is centered at the point $z = z_0$, then the complex plane near $z_0$ locally splits into $2k$ sectors of equal angle, alternating between sectors in which $|p(z)| > |p(z_0)|$ and sectors in which $|p(z)| < |p(z_0)|$. In our subsequent research, we found that this symmetry, which Kalantari formalizes as the Geometric Modulus Principle, is retained (under appropriate modifications) for much larger classes of functions, in particular holomorphic functions as well as harmonic functions of two real variables.This dissertation continues our work in several respects. First, we expand the Geometric Modulus Principle to a broader class of analytic functions, the so-called \extit{approximately harmonic functions}, that behaves much like the class of harmonic functions with respect to ring operations. We then define the \extit{geometric modulus property}, enjoyed by a larger-still class of functions, which formalizes the idea of the sign of a function "undulating" in sectors around a point of its domain. If a function has the geometric modulus property and is of order $m$ as an analytic function at a point, then its $m.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798790631139Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Complex analysisIndex Terms--Genre/Form:

542853
Electronic books.

Extending the Geometric Modulus Principle.
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100 1 $a Hohertz, Matthew Ryan. $3 3704028
245 1 0 $a Extending the Geometric Modulus Principle.
264 0 $c 2022
300 $a 1 online resource (54 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 83-08, Section: B.
500 $a Advisor: Feehan, Paul.
502 $a Thesis (Ph.D.)--Rutgers The State University of New Jersey, School of Graduate Studies, 2022.
504 $a Includes bibliographical references
520 $a In a 2011 paper, Kalantari observes that complex polynomials exhibit a certain symmetry with respect to argument at every point. To wit, if the polynomial $p(z)$ has order $k$ as an analytic function whose germ is centered at the point $z = z_0$, then the complex plane near $z_0$ locally splits into $2k$ sectors of equal angle, alternating between sectors in which $|p(z)| > |p(z_0)|$ and sectors in which $|p(z)| < |p(z_0)|$. In our subsequent research, we found that this symmetry, which Kalantari formalizes as the Geometric Modulus Principle, is retained (under appropriate modifications) for much larger classes of functions, in particular holomorphic functions as well as harmonic functions of two real variables.This dissertation continues our work in several respects. First, we expand the Geometric Modulus Principle to a broader class of analytic functions, the so-called \extit{approximately harmonic functions}, that behaves much like the class of harmonic functions with respect to ring operations. We then define the \extit{geometric modulus property}, enjoyed by a larger-still class of functions, which formalizes the idea of the sign of a function "undulating" in sectors around a point of its domain. If a function has the geometric modulus property and is of order $m$ as an analytic function at a point, then its $m.
520 $a {th}$ derivative with respect to radius is a trigonometric polynomial that behaves like a sine function; we call such trigonometric polynomials \extit{sinusoidal}, devoting a section of the appendix to their properties. We conclude with some applications of our work and questions for future study.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Applied mathematics. $3 2122814
653 $a Complex analysis
653 $a Geometry of surfaces
653 $a Harmonic functions
653 $a Polynomials
655 7 $a Electronic books. $2 lcsh $3 542853
690 $a 0405
690 $a 0642
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 783688
710 2 $a Rutgers The State University of New Jersey, School of Graduate Studies. $b Mathematics. $3 3698280
773 0 $t Dissertations Abstracts International $g 83-08B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28962805 $z click for full text (PQDT)