Introductory Topics in Distributions over Binary Test Functions
General Mathematics
2007-05-23 v1
Abstract
We note with B2 the Boole algebra with two elements. We define for the R->B2 functions the limits, the derivatives, the differentiability, the test functions, the integrals. We also define the distributions over the space of these test functions, the regular and the singular distributions, the support sets of the distributions. We also define for the RxR->{0,1} functions the test functions and the distributions over them. The direct product of the distributions is presented, as well as the convolution algebras of distributions. Generalizations of the binary test functions and of the distributions over them are given.
Cite
@article{arxiv.math/0110335,
title = {Introductory Topics in Distributions over Binary Test Functions},
author = {Serban E. Vlad},
journal= {arXiv preprint arXiv:math/0110335},
year = {2007}
}
Comments
the MSC-class was chosen by analogy: we refer to binary valued functions here, not to real valued functions