Invariant mean value property and harmonic functions

2005 ◽  
Vol 50 (14) ◽  
pp. 1049-1059 ◽  
Author(s):  
Jinman Kim ◽  
M. W. Wong
Keyword(s):  
Harmonic Functions ◽  
Mean Value ◽  
Invariant Mean ◽  
Mean Value Property

scholarly journals Hyperbolic harmonic functions and the associated integral equations

2015 ◽  
Vol 53 (1) ◽  
pp. 37-56
Author(s):  
Namita Das ◽  
Rajendra Prasad Lal
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Integral Equations ◽  
Harmonic Functions ◽  
Numerical Solutions ◽  
Mean Value ◽  
Invariant Mean ◽  
Mean Value Property ◽  
Hyperbolic Harmonic Functions

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.

scholarly journals On the mean value property of superharmonic and subharmonic functions

2006 ◽  
Vol 2006 ◽  
pp. 1-3
Author(s):  
Robert Dalmasso
Keyword(s):  
Harmonic Functions ◽  
Mean Value ◽  
Subharmonic Functions ◽  
Mean Value Property ◽  
The Mean

We prove a converse of the mean value property for superharmonic and subharmonic functions. The case of harmonic functions was treated by Epstein and Schiffer.

On the Inverse mean value Property of Harmonic Functions on Strips

1992 ◽  
Vol 24 (6) ◽  
pp. 559-564 ◽  
Author(s):  
M. Goldstein ◽  
W. Haussmann ◽  
L. Rogge
Keyword(s):  
Harmonic Functions ◽  
Mean Value ◽  
Mean Value Property

scholarly journals On the mean value property of fractional harmonic functions

2020 ◽  
Vol 201 ◽  
pp. 112112
Author(s):  
Claudia Bucur ◽  
Serena Dipierro ◽  
Enrico Valdinoci
Keyword(s):  
Harmonic Functions ◽  
Mean Value ◽  
Mean Value Property ◽  
The Mean

On the mean-value property of harmonic functions

1965 ◽  
Vol 14 (1) ◽  
pp. 109-111 ◽  
Author(s):  
Bernard Epstein ◽  
M. M. Schiffer
Keyword(s):  
Harmonic Functions ◽  
Mean Value ◽  
Mean Value Property ◽  
The Mean
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