POTENTIAL WITH CLOSED SYSTEMS OF (TRIAL) FUNCTIONS
Willi Freeden · 1980
Summary Let S be the (regular) boundary-surface of an exterior region E e in Euclidean space tR 3 (for instance : sphere, ellipsoid, geoid, earth's surface). Denote by I ¢> n I a countable, linearly independent system of trial functions (e.g., solid spherical harmonics or certain singularity functions) which are harmonic in some domain containing Ee uS . It is the purpose of this paper to show that the restrictions I 'Pn I of the functions I cp n I on S form a closed system in the space C ( S), i.e. any [unction f, defined and continuous on S , can be approximated uniformly by a linear combination of the functions op 0 .