Wavelet analysis and the geometry of Euclidean domains (Q1184389)

This interesting paper is devoted to the so-called wavelet analysis. The authors give a brief overview of this new branch of harmonic analysis in general and discuss the well-known distribution representation of geometric domains and their boundaries. These two points of view are combined to provide explicit ``wavelet'' formulas for boundary integrals which appear in weak solutions of partial differential equations. The exterior derivative of the characteristic function of a domain is represented in an infinite series of compactly supported wavelet functions whose supports intersect the geometric boundary.