Illinois Journal of Mathematics

Approximation on the boundary and sets of determination for harmonic functions

Stephen J. Gardiner and Jordi Pau

Full-text: Open access

Abstract

Let $E$ be a subset of a domain $\Omega $ in Euclidean space. This paper deals with the representation, or approximation, of functions on the boundary of $\Omega $ by sums of Poisson, Green or Martin kernels associated with the set $E$, and with the related issue of whether $E$ can be used to determine the suprema of certain harmonic functions on $\Omega $. The results address several questions raised by Hayman.

Article information

Source
Illinois J. Math., Volume 47, Number 4 (2003), 1115-1136.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138094

Digital Object Identifier
doi:10.1215/ijm/1258138094

Mathematical Reviews number (MathSciNet)
MR2036993

Zentralblatt MATH identifier
1050.31003

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

Citation

Gardiner, Stephen J.; Pau, Jordi. Approximation on the boundary and sets of determination for harmonic functions. Illinois J. Math. 47 (2003), no. 4, 1115--1136. doi:10.1215/ijm/1258138094. https://projecteuclid.org/euclid.ijm/1258138094


Export citation