Coleção CLE: Vol 89 - Axiomatic Theory of Distributions

Axiomatic Theory of Distributions

This monograph presents, essentially, the definition of an axiomatic structure, which we call "S-space", and proofs of two "extension" theorems associated to it that, in turn, not only allow obtaining as a particular case (associated to a particular model of the S-space structure) axiomatics that categorically define the notions of distributions and its derivatives such as introduced by Laurent Schwartz, but also, and mainly, due to its abstract nature, explicit a structural environment conceptually very simple where other generalizations, analogous the one promoted to differential calculus by the theory of distributions, can, in principle, extend.