## Real Analysis Exchange

### Harmonic Singularity at Infinity in ${\mathbb R}^n$

#### Abstract

Some properties of harmonic functions defined outside a compact set in ${\mathbb R}^n$ are given. From them is deduced a generalized form of Liouville’s theorem in ${\mathbb R}^n$ which is known to be equivalent to an improved version of the classical Bôcher theorem on harmonic point singularities.

#### Article information

Source
Real Anal. Exchange, Volume 23, Number 2 (1999), 471-476.

Dates
First available in Project Euclid: 14 May 2012

https://projecteuclid.org/euclid.rae/1337001359

Mathematical Reviews number (MathSciNet)
MR1639952

Zentralblatt MATH identifier
0938.31003

Subjects
Primary: 31B05: Harmonic, subharmonic, superharmonic functions

#### Citation

Anandam, V.; Damlakhi, M. Harmonic Singularity at Infinity in ${\mathbb R}^n$. Real Anal. Exchange 23 (1999), no. 2, 471--476. https://projecteuclid.org/euclid.rae/1337001359