Construction of Planar Harmonic Functions

Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk can be written in the form f=h+g¯, where h and g are analytic in the open unit disk. The functions h and g are called the analytic and coanalytic parts of f, respectively. In this paper, we construct cert...

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Main Authors: Jay M. Jahangiri, Herb Silverman, Evelyn M. Silvia
Format: Article
Language:English
Published: Wiley 2007-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2007/70192
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author Jay M. Jahangiri
Herb Silverman
Evelyn M. Silvia
author_facet Jay M. Jahangiri
Herb Silverman
Evelyn M. Silvia
author_sort Jay M. Jahangiri
collection DOAJ
description Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk can be written in the form f=h+g¯, where h and g are analytic in the open unit disk. The functions h and g are called the analytic and coanalytic parts of f, respectively. In this paper, we construct certain planar harmonic maps either by varying the coanalytic parts of harmonic functions that are known to be harmonic starlike or by adjoining analytic univalent functions with coanalytic parts that are related or derived from the analytic parts.
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series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-91a1d197388f44c0b21f1efbfc0557a62025-02-03T05:58:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/7019270192Construction of Planar Harmonic FunctionsJay M. Jahangiri0Herb Silverman1Evelyn M. Silvia2Department of Mathematical Sciences, Kent State University, Burton 44021-9500, OH, USADepartment of Mathematics, College of Charleston, Charleston 29424, SC, USADepartment of Mathematics, University of California at Davis, Davis 95616-8633, CA, USAComplex-valued harmonic functions that are univalent and sense-preserving in the open unit disk can be written in the form f=h+g¯, where h and g are analytic in the open unit disk. The functions h and g are called the analytic and coanalytic parts of f, respectively. In this paper, we construct certain planar harmonic maps either by varying the coanalytic parts of harmonic functions that are known to be harmonic starlike or by adjoining analytic univalent functions with coanalytic parts that are related or derived from the analytic parts.http://dx.doi.org/10.1155/2007/70192
spellingShingle Jay M. Jahangiri
Herb Silverman
Evelyn M. Silvia
Construction of Planar Harmonic Functions
International Journal of Mathematics and Mathematical Sciences
title Construction of Planar Harmonic Functions
title_full Construction of Planar Harmonic Functions
title_fullStr Construction of Planar Harmonic Functions
title_full_unstemmed Construction of Planar Harmonic Functions
title_short Construction of Planar Harmonic Functions
title_sort construction of planar harmonic functions
url http://dx.doi.org/10.1155/2007/70192
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AT herbsilverman constructionofplanarharmonicfunctions
AT evelynmsilvia constructionofplanarharmonicfunctions