Unbounded harmonic functions on
homogeneous manifolds of negative curvature
Colloquium Mathematicum, Tome 91 (2002) no. 1, pp. 99-121
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We study unbounded harmonic functions for a second order differential operator on a homogeneous manifold of negative curvature which is a semidirect product of a nilpotent Lie group $N$ and $A={\mathbb R}^+.$ We prove that if $F$ is harmonic and satisfies some growth condition then $F$ has an asymptotic expansion as $a\to 0$ with coefficients from ${\cal D}^\prime (N).$ Then we single out a set of at most two of these coefficients which determine $F.$
Then using asymptotic expansions we are able to prove some theorems answering partially the following question.
Is a given harmonic function the Poisson integral of “something" from the boundary $N$?
Keywords:
study unbounded harmonic functions second order differential operator homogeneous manifold negative curvature which semidirect product nilpotent lie group mathbb prove harmonic satisfies growth condition has asymptotic expansion coefficients cal prime single out set these coefficients which determine using asymptotic expansions able prove theorems answering partially following question given harmonic function poisson integral something boundary
Affiliations des auteurs :
Richard Penney 1 ; Roman Urban 2
@article{10_4064_cm91_1_8,
author = {Richard Penney and Roman Urban},
title = {Unbounded harmonic functions on
homogeneous manifolds of negative curvature},
journal = {Colloquium Mathematicum},
pages = {99--121},
publisher = {mathdoc},
volume = {91},
number = {1},
year = {2002},
doi = {10.4064/cm91-1-8},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm91-1-8/}
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%0 Journal Article %A Richard Penney %A Roman Urban %T Unbounded harmonic functions on homogeneous manifolds of negative curvature %J Colloquium Mathematicum %D 2002 %P 99-121 %V 91 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/cm91-1-8/ %R 10.4064/cm91-1-8 %G en %F 10_4064_cm91_1_8
Richard Penney; Roman Urban. Unbounded harmonic functions on homogeneous manifolds of negative curvature. Colloquium Mathematicum, Tome 91 (2002) no. 1, pp. 99-121. doi: 10.4064/cm91-1-8
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