On the mean value property of finely harmonic and finely hyperharmonic functions

1990 ◽  
Vol 39 (2-3) ◽  
pp. 198-203 ◽  
Author(s):  
B. Fuglede
Keyword(s):  
Mean Value ◽  
Mean Value Property ◽  
The Mean

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.

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

The Mean-Value Property

2015 ◽  
Vol 37 (2) ◽  
pp. 9-16
Author(s):  
Vilmos Totik
Keyword(s):  
Mean Value ◽  
Mean Value Property ◽  
The Mean

scholarly journals Lp-functions satisfying the mean value property on homogeneous spaces

1994 ◽  
Vol 56 (3) ◽  
pp. 384-390 ◽  
Author(s):  
A. Sitaram ◽  
G. A. Willis
Keyword(s):  
Homogeneous Spaces ◽  
Mean Value ◽  
Mean Value Property ◽  
Zero Function ◽  
The Mean

AbstractIt is proved that on certain kinds of homogeneous spaces, the only Lp function, 1≤ p < ∞, satisfying the mean value property is the zero function.

Functions Satisfying the Mean Value Property

1962 ◽  
Vol 102 (1) ◽  
pp. 167 ◽  
Author(s):  
Avner Friedman ◽  
Walter Littman
Keyword(s):  
Mean Value ◽  
Mean Value Property ◽  
The Mean

MEAN VALUE PROPERTY OF HARMONIC FUNCTION ON THE HIGHER-DIMENSIONAL SIERPINSKI GASKET

Fractals ◽  
2020 ◽  
Vol 28 (05) ◽  
pp. 2050077
Author(s):  
YIPENG WU ◽  
ZHILONG CHEN ◽  
XIA ZHANG ◽  
XUDONG ZHAO
Keyword(s):  
Harmonic Function ◽  
Harmonic Functions ◽  
Sierpinski Gasket ◽  
Mean Value ◽  
Sierpiński Gasket ◽  
Mean Value Property ◽  
Average Value ◽  
Higher Dimensional ◽  
The Mean

Harmonic functions possess the mean value property, that is, the value of the function at any point is equal to the average value of the function in a domain that contain this point. It is a very attractive problem to look for analogous results in the fractal context. In this paper, we establish a similar results of the mean value property for the harmonic functions on the higher-dimensional Sierpinski gasket.

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