Heaviside calculus with no Laplace transform

Abstract

In this paper, we settle down the bases of a general formal calculus which does not require precautions concerning the convergence of the Laplace function and derivation with respect to a parameter. We also show that divergent series can play the role of generalized images. This approach avoids the introduction of abstract spaces (distributions, hyperdistributions, etc.). This calculation, however, applies to physical systems with Dirac functions, Dirac's combs, etc. Our strategy consists of the introduction of words of an enriched mathematical language in order to assert the partial indetermination of Dirac improper functions, rather than to affirm their existence in a functional space.

Keywords:

• Laplace transform
• Heaviside calculus
• Delta function
• Regularization

Additional information

Notes on contributors

Yves Péraire

Email: [email protected]