scholarly journals Asymptotic mean value formula for sub- p -harmonic functions on the Heisenberg group

2013 ◽  
Vol 264 (9) ◽  
pp. 2177-2196 ◽  
Author(s):  
Hairong Liu ◽  
Xiaoping Yang
Keyword(s):  
Heisenberg Group ◽  
Harmonic Functions ◽  
Mean Value ◽  
Mean Value Formula

scholarly journals Almansi Theorem and Mean Value Formula for Quaternionic Slice-regular Functions

2020 ◽  
Vol 30 (4) ◽  
Author(s):  
Alessandro Perotti
Keyword(s):  
Harmonic Functions ◽  
Mean Value ◽  
Zonal Harmonic ◽  
Slice Regular Functions ◽  
Regular Functions ◽  
Quaternionic Polynomials ◽  
Mean Value Formula

Abstract We prove an Almansi Theorem for quaternionic polynomials and extend it to quaternionic slice-regular functions. We associate to every such function f, a pair $$h_1$$ h 1 , $$h_2$$ h 2 of zonal harmonic functions such that $$f=h_1-\bar{x} h_2$$ f = h 1 - x ¯ h 2 . We apply this result to get mean value formulas and Poisson formulas for slice-regular quaternionic functions.

scholarly journals On the characterization of $p$-harmonic functions on the Heisenberg group by mean value properties

2014 ◽  
Vol 34 (7) ◽  
pp. 2779-2793 ◽  
Author(s):  
Fausto Ferrari ◽  
◽  
Qing Liu ◽  
Juan Manfredi ◽  
Keyword(s):  
Heisenberg Group ◽  
Harmonic Functions ◽  
Mean Value

scholarly journals Some Remarks on Harmonic Functions in Minkowski Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 196
Author(s):  
Songting Yin
Keyword(s):  
Harmonic Function ◽  
Minkowski Space ◽  
Harmonic Functions ◽  
Mean Value ◽  
Mean Value Property ◽  
Minkowski Spaces ◽  
The Mean ◽  
Mean Value Formula

We prove that in Minkowski spaces, a harmonic function does not necessarily satisfy the mean value formula. Conversely, we also show that a function satisfying the mean value formula is not necessarily a harmonic function. Finally, we conclude that in a Minkowski space, if all harmonic functions have the mean value property or any function satisfying the mean value formula must be a harmonic function, then the Minkowski space is Euclidean.

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.

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