Hyperbolic harmonic functions and the associated integral equations

Namita Das; Rajendra Prasad Lal

doi:10.1515/awutm-2015-0003

.blurhash-client-img { display: none !important; }

Hyperbolic harmonic functions and the associated integral equations

Annals of West University of Timisoara - Mathematics and Computer Science

Volume 53 (2015): Issue 1 (July 2015)

By: Namita Das and Rajendra Prasad Lal

Open Access

|Dec 2015

Abstract

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.

References

[1] Ahern P. Flores M. and Rudin W., An invariant volume-mean-value property, J.Funct. Anal., 111, (1993), 380–397.10.1006/jfan.1993.1018
Search in Google Scholar
[2] Atkinson K.E., An Introduction to Numerical Analysis, John Wiley, New York, 1988.
Search in Google Scholar
[3] Ahlfors L., Mobius transformations in several dimensions, University of Minnesota, 1981.
Search in Google Scholar
[4] Axler S. and Cuckovic Z., Commuting Toeplitz operators with harmonic symbols, Integral Equations Operator Theory, 14, (1991), 1–12.10.1007/BF01194925
Search in Google Scholar
[5] Erdelyi A. Magnus W. Oberhettinger F. and Tricomi F.G., Higher Transcen- dental Functions, McGraw-Hill, New York, 1955.
Search in Google Scholar
[6] Gelfand I. M., Spherical functions on symmetric Riemannian spaces, Dokl. Akad. Nauk SSSR, 70, (1950), 5–8.
Search in Google Scholar
[7] Jevtic M., Fixed points of an integral operator, J. Anal. Math., 91, (2003), 123–141.10.1007/BF02788784
Search in Google Scholar
[8] Whittaker E. and Watson G., A course of Modern Analysis, Cambridge University Press, 1988.
Search in Google Scholar
[9] Yi J.S., A characterization of the functions fixed by a class of integral operators, 1995.
Search in Google Scholar

Articles in this issue

DOI: https://doi.org/10.1515/awutm-2015-0003 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293

Journal RSS Feed

Language: English

Page range: 37 - 56

Submitted on: Sep 9, 2014

Accepted on: Jul 5, 2015

Published on: Dec 12, 2015

Published by: West University of Timisoara

In partnership with: Paradigm Publishing Services

Publication frequency: Volume open

Keywords:

Bergman space,

Berezin transform,

hyperbolic harmonic functions,

invariant mean-value property,

integral equations

Related subjects:

Mathematics,

General mathematics

© 2015 Namita Das, Rajendra Prasad Lal, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 53 (2015): Issue 1 (July 2015)