MULTIPLICATION OF SCHWARTZ DISTRIBUTIONS AND COLOMBEAU GENERALIZED FUNCTIONS

The dierential -algebra G( m ) of generalized functions of J.- F. Colombeau contains the spaceD 0 ( m ) of Schwartz distributions as a -vector subspace and the notion of 'association' in that algebra generalizes the equality inD 0 ( m ). This is particularly useful for eval- uation of distribution products, as they are embedded in G( m ), in terms of distributions again. The paper is devoted to results on partic- ular products of distributions with coinciding singularities, as well as to a general property of Colombeau product of distributions together with some applications. All formulas obtained, when restricted to dimen- sion one, are easily transformed into the setting of regularized model products in classical distribution theory.