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An Embedding of Schwartz Distributions in the Algebra of Asymptotic Functions

M. Oberguggenberger, T. Todorov

Abstract

We present a solution of the problem of multiplication of Schwartz distributions by embedding the space of distributions into a differential algebra of generalized functions, called in the paper ``asymptotic function'', similar to but different from J. F. Colombeau's algebras of new generalized functions.

An Embedding of Schwartz Distributions in the Algebra of Asymptotic Functions

Abstract

We present a solution of the problem of multiplication of Schwartz distributions by embedding the space of distributions into a differential algebra of generalized functions, called in the paper ``asymptotic function'', similar to but different from J. F. Colombeau's algebras of new generalized functions.
Paper Structure (5 sections, 48 equations)

This paper contains 5 sections, 48 equations.

Table of Contents

  1. Introduction
  2. Test Functions and Their Moments
  3. Nonstandard Delta Functions
  4. The Algebra of Asymptotic Functions
  5. Embedding of Schwartz Distributions