Hyperbolic harmonic functions and the associated integral equations
In this paper we consider a class of integral equations associated with the invariant mean value property of hyperbolic harmonic functions. We have shown that nonconstant solutions of these integral equations are functions of unbounded variations and do not attain their supremum or infimum on [0; 1)...
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2015-07-01
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| Series: | Annals of the West University of Timisoara: Mathematics and Computer Science |
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| Online Access: | https://doi.org/10.1515/awutm-2015-0003 |
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doaj-88ae89569bed4576b30bcc785cd2b7f52021-09-06T19:40:23ZengSciendoAnnals of the West University of Timisoara: Mathematics and Computer Science1841-33072015-07-01531375610.1515/awutm-2015-0003awutm-2015-0003Hyperbolic harmonic functions and the associated integral equationsDas Namita0Lal Rajendra Prasad1P.G. Department of Mathematics Utkal University Vanivihar, Bhubaneswar, 751004, Odisha, IndiaDepartment of Computer and Information Sciences University of Hyderabad Hyderabad, India-500046In this paper we consider a class of integral equations associated with the invariant mean value property of hyperbolic harmonic functions. We have shown that nonconstant solutions of these integral equations are functions of unbounded variations and do not attain their supremum or infimum on [0; 1): We present an algorithm to obtain numerical solutions of these integral equations. We also consider the equivalent ordinary differential equations and used MATLAB to obtain numerical solutions of these differential equations.https://doi.org/10.1515/awutm-2015-0003bergman spaceberezin transformhyperbolic harmonic functionsinvariant mean-value propertyintegral equations |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Das Namita Lal Rajendra Prasad |
| spellingShingle |
Das Namita Lal Rajendra Prasad Hyperbolic harmonic functions and the associated integral equations Annals of the West University of Timisoara: Mathematics and Computer Science bergman space berezin transform hyperbolic harmonic functions invariant mean-value property integral equations |
| author_facet |
Das Namita Lal Rajendra Prasad |
| author_sort |
Das Namita |
| title |
Hyperbolic harmonic functions and the associated integral equations |
| title_short |
Hyperbolic harmonic functions and the associated integral equations |
| title_full |
Hyperbolic harmonic functions and the associated integral equations |
| title_fullStr |
Hyperbolic harmonic functions and the associated integral equations |
| title_full_unstemmed |
Hyperbolic harmonic functions and the associated integral equations |
| title_sort |
hyperbolic harmonic functions and the associated integral equations |
| publisher |
Sciendo |
| series |
Annals of the West University of Timisoara: Mathematics and Computer Science |
| issn |
1841-3307 |
| publishDate |
2015-07-01 |
| description |
In this paper we consider a class of integral equations associated with the invariant mean value property of hyperbolic harmonic functions. We have shown that nonconstant solutions of these integral equations are functions of unbounded variations and do not attain their supremum or infimum on [0; 1): We present an algorithm to obtain numerical solutions of these integral equations. We also consider the equivalent ordinary differential equations and used MATLAB to obtain numerical solutions of these differential equations. |
| topic |
bergman space berezin transform hyperbolic harmonic functions invariant mean-value property integral equations |
| url |
https://doi.org/10.1515/awutm-2015-0003 |
| work_keys_str_mv |
AT dasnamita hyperbolicharmonicfunctionsandtheassociatedintegralequations AT lalrajendraprasad hyperbolicharmonicfunctionsandtheassociatedintegralequations |
| _version_ |
1717768584320516096 |