The sequence of ideas in a re-discovery of the Colombeau algebras
Abstract
Description
This is a gentle introduction to Colombeau nonlinear generalized functions, a generalization of the concept of distributions such that distributions can freely be multiplied. It is intended to physicists and applied mathematicians who prefer a `step-by-step approach' to a `top-down indoctrination.'
No particular prerequisite knowledge is necessary -- and in less than one hour you should know everything you need to know and were afraid to ask about Colombeau algebras and their applications in physics...
A selected bibliography is appended, giving examples of applications to partial differential and wave equations, electrodynamics, hydrodynamics, general relativity, and quantum field theory.
28 pages. Minor corrections and additional references
28 pages. Minor corrections and additional references