Colombeau J.F. Elementary Introduction to New Generalized Functions

North-Holland Publishing, 1985. - 282 pages.In our previous book "New Generalized Functions and Multiplication of Distributions" North-Holland Math. Studies 84, 1984 (referred to below as "N.G.F.") we introduced "new generalized functions" in order to explain heuristic computations of Physics and to give a meaning to any finite product of distributions.Our aim in this book is to present these generalized functions in a direct and elementary way and to extend the approach initiated in N.G.F. There we explained how we were led to define these generalized functions using Distribution Theory as a starting point. Then some concepts of the theory of locally convex spaces were needed. Indeed we will see that they can be presented in a more direct and easier way.