CONSTRUCTIVE DESCRIPTION OF FUNCTION CLASSES ON SURFACES IN R^3 AND R^4

Abstract

Functional classes on a curve in a plane (a partial case of a spatial curve) can be described by the approximation speed by functions that are harmonic in three-dimensional neighbourhoods of the curve. No constructive description of functional classes on rather general surfaces in R 3 and R 4 has been presented in literature so far. The main result of the paper is Theorem 1.

Keywords

• constructive description
• rational functions
• harmonic functions
• pseudoharmonic functions