1. Global approximation in harmonic spaces
- Author
-
Stephen J. Gardiner, Kohur GowriSankaran, and Myron Goldstein
- Subjects
Compact space ,Subharmonic function ,Harmonic space ,Applied Mathematics ,General Mathematics ,Mathematical analysis ,MathematicsofComputing_GENERAL ,Neighbourhood (graph theory) ,Harmonic (mathematics) ,Mathematics - Abstract
This paper characterizes, in terms of thinness, compact sets K in a suitable harmonic space Ω \Omega which have the following property: functions which are harmonic (resp. continuous and superharmonic) on a neighbourhood of K can be uniformly approximated on K by functions which are harmonic (resp. continuous and superharmonic) on Ω \Omega . The corresponding problems of approximating functions which are continuous on K and harmonic (resp. superharmonic) on the interior K ˚ \mathring {K} are also solved.
- Published
- 1994