Multiplication of Distributions in One Dimension: Possible Approaches and Applications to \u3b4-Function and Its Derivatives

We introduce a new class of multiplications of distributions in one dimension merging two different regularizations of distributions. Some of the features of these multiplications are discussed in detail. We use our theory to study a number of examples, involving products between Dirac delta functions and its successive derivatives. \ua9 1995 Academic Press. All rights reserved