An intrinsic theory of Colombeau algebras

Abstract

The Theory of Colombeau Generalized Functions has under gone a rapid grow during the last few years. It is establishing itself as a useful tool in the fields of Analyses, Geometry and Physics. The algebraic approach, started by researchers of IME-USP, has become one of the principal directions for intrinsic tools development making possible further theoretical developments. At the same time, intrinsic analytical and geometrical tools are also being developed. Making one theory out of these tools is becoming a necessity for the global development of the Theory of Generalized Functions. One of the objectives of this research project, in collaboration with Prof. Dr. Jean-François Colombeau, is to make progress in this direction, which was started by the DIANA Research group of Prof. Prod. Michael Kunzinger. (AU)