Unbounded harmonic functions on homogeneous manifolds of negative curvature

Richard Penney; Roman Urban

Colloquium Mathematicae (2002)

  • Volume: 91, Issue: 1, page 99-121
  • ISSN: 0010-1354

Abstract

top
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 = ℝ⁺. We prove that if F is harmonic and satisfies some growth condition then F has an asymptotic expansion as a → 0 with coefficients from 𝓓'(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?

How to cite

top

Richard Penney, and Roman Urban. "Unbounded harmonic functions on homogeneous manifolds of negative curvature." Colloquium Mathematicae 91.1 (2002): 99-121. <http://eudml.org/doc/283895>.

@article{RichardPenney2002,
abstract = { 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 = ℝ⁺. We prove that if F is harmonic and satisfies some growth condition then F has an asymptotic expansion as a → 0 with coefficients from 𝓓'(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? },
author = {Richard Penney, Roman Urban},
journal = {Colloquium Mathematicae},
keywords = {unbounded harmonic function; asymptotic expansion; Poisson integral},
language = {eng},
number = {1},
pages = {99-121},
title = {Unbounded harmonic functions on homogeneous manifolds of negative curvature},
url = {http://eudml.org/doc/283895},
volume = {91},
year = {2002},
}

TY - JOUR
AU - Richard Penney
AU - Roman Urban
TI - Unbounded harmonic functions on homogeneous manifolds of negative curvature
JO - Colloquium Mathematicae
PY - 2002
VL - 91
IS - 1
SP - 99
EP - 121
AB - 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 = ℝ⁺. We prove that if F is harmonic and satisfies some growth condition then F has an asymptotic expansion as a → 0 with coefficients from 𝓓'(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?
LA - eng
KW - unbounded harmonic function; asymptotic expansion; Poisson integral
UR - http://eudml.org/doc/283895
ER -

NotesEmbed ?

top

You must be logged in to post comments.