# Ouroboros Functionals, Families of Ouroboros Functions, and Their Relationship to Partial Differential Equations and Probability Theory

• Published in 2021
In the collection
Previously, we have introduced a very small number of examples of what we call Ouroboros functions. Using our already established theory of Ouroboros spaces and their functions, we will provide a set of families of Ouroboros functions that bolster our overall understanding of the Ouroboros spaces. From here, we extend the theory of Ouroboros functions by introducing Ouroboros functionals and Ouroboros functional spaces. Furthermore, we re-frame the expected value of a random variable as an Ouroboros functional, which proves to be more intuitive in view of probabilistic measure theory. We then show that these Ouroboros functions have additional applications, as they are general solutions to certain elementary linear first order partial differential equations (PDEs). We conclude by elaborating upon this connection and discussing future endeavors, which will be centered on answering a given hypothesis.

### BibTeX entry

@article{OuroborosFunctionalsFamiliesofOuroborosFunctionsandTheirRelationshiptoPartialDifferentialEquationsandProbabilityTheory,
title = {Ouroboros Functionals, Families of Ouroboros Functions, and Their  Relationship to Partial Differential Equations and Probability Theory},
abstract = {Previously, we have introduced a very small number of examples of what we
call Ouroboros functions. Using our already established theory of Ouroboros
spaces and their functions, we will provide a set of families of Ouroboros
functions that bolster our overall understanding of the Ouroboros spaces. From
here, we extend the theory of Ouroboros functions by introducing Ouroboros
functionals and Ouroboros functional spaces. Furthermore, we re-frame the
expected value of a random variable as an Ouroboros functional, which proves to
be more intuitive in view of probabilistic measure theory. We then show that
these Ouroboros functions have additional applications, as they are general
solutions to certain elementary linear first order partial differential
equations (PDEs). We conclude by elaborating upon this connection and
discussing future endeavors, which will be centered on answering a given
hypothesis.},
url = {http://arxiv.org/abs/2106.04680v1 http://arxiv.org/pdf/2106.04680v1},
year = 2021,
author = {Nathan Thomas Provost},
comment = {},
urldate = {2021-08-29},
archivePrefix = {arXiv},
eprint = {2106.04680},
primaryClass = {math.FA},
collections = {attention-grabbing-titles}
}