Harmonic Functions on Hermitian Hyperbolic Space

1969 ◽  
Vol 135 ◽  
pp. 507 ◽  
Author(s):  
Adam Koranyi
Keyword(s):  
Hyperbolic Space ◽  
Harmonic Functions

Harmonic Spinors on Hyperbolic Space

1993 ◽  
Vol 36 (3) ◽  
pp. 257-262 ◽  
Author(s):  
Pierre-Yves Gaillard
Keyword(s):  
Differential Equations ◽  
Symmetric Space ◽  
Representation Theory ◽  
Hyperbolic Space ◽  
Harmonic Functions ◽  
Short Note ◽  
Harmonic Forms ◽  
Semisimple Symmetric Space ◽  
Invariant Differential ◽  
Harmonic Spinors

AbstractThe purpose for this short note is to describe the space of harmonic spinors on hyperbolicn-spaceHn. This is a natural continuation of the study of harmonic functions onHnin [Minemura] and [Helgason]—these results were generalized in the form of Helgason's conjecture, proved in [KKMOOT],—and of [Gaillard 1, 2], where harmonic forms onHnwere considered. The connection between invariant differential equations on a Riemannian semisimple symmetric spaceG/Kand homological aspects of the representation theory ofG, as exemplified in (8) below, does not seem to have been previously mentioned. This note is divided into three main parts respectively dedicated to the statement of the results, some reminders, and the proofs. I thank the referee for having suggested various improvements.

scholarly journals Functions with finite Dirichlet sum of order p and quasi-monomorphisms of infinite graphs

2012 ◽  
Vol 207 ◽  
pp. 95-138 ◽  
Author(s):  
Tae Hattori ◽  
Atsushi Kasue
Keyword(s):  
Hyperbolic Space ◽  
Harmonic Functions ◽  
Space Form ◽  
Infinite Graph ◽  
Infinite Graphs ◽  
Infinite Networks ◽  
Hyperbolic Space Form

AbstractIn this paper, we study some potential theoretic properties of connected infinite networks and then investigate the space of p-Dirichlet finite functions on connected infinite graphs, via quasi-monomorphisms. A main result shows that if a connected infinite graph of bounded degrees possesses a quasi-monomorphism into the hyperbolic space form of dimension n and it is not p-parabolic for p > n - 1, then it admits a lot of p-harmonic functions with finite Dirichlet sum of order p.

scholarly journals Universal harmonic functions on the hyperbolic space

2010 ◽  
Vol 121 (1) ◽  
pp. 93-105 ◽  
Author(s):  
Athanassia Bacharoglou ◽  
George Stamatiou
Keyword(s):  
Hyperbolic Space ◽  
Harmonic Functions

Distance Distribution between Complex Network Nodes in Hyperbolic Space

2016 ◽  
Vol 25 (3) ◽  
pp. 223-236 ◽  
Author(s):  
Gregorio Alanis-Lobato ◽  
Miguel A. Andrade-Navarro ◽  
Keyword(s):  
Complex Network ◽  
Hyperbolic Space ◽  
Distance Distribution ◽  
Network Nodes

On the Radial Symmetry Property for Harmonic Functions

2020 ◽  
Vol 64 (10) ◽  
pp. 9-19
Author(s):  
V. V. Volchkov ◽  
Vit. V. Volchkov
Keyword(s):  
Harmonic Functions ◽  
Symmetry Property ◽  
Radial Symmetry
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