[3] **viXra:1907.0491 [pdf]**
*submitted on 2019-07-25 19:05:50*

**Authors:** Josh O'Connor

**Comments:** 18 Pages.

This paper generalises the limit definitions of calculus to define differintegrals of complex order, calculates some differintegrals of elementary functions, and introduces the notion of a fractional differential equation. An application to quantum theory is explored, and we conclude with some operator algebra. Functions in this paper will only have one variable.

**Category:** Functions and Analysis

[2] **viXra:1907.0454 [pdf]**
*submitted on 2019-07-25 04:57:09*

**Authors:** Naum E. Salis

**Comments:** 15 Pages.

The purpose of this paper is to try to replicate what happens in C on spaces where there are more then one of immaginary units. All these spaces, in our definition, will have the same Hilbert structure. At first we will introduce the sum and product operations on C(H):=RxH (where H is an Hilbert space), then we'll investigate on its algebraic properties. In our construction we lose only the associative of multiplication regardless of H, exept when dim H=1 (in this case RxH = C), and this is why we say "weak extension". One of the most important result of this study is the Weak Integrity Theorem according to which in particular conditions there exist zero divisors. The next result is the Foundamental Theorem according to which for all z in C(H) there exists w in C(H) such that z=w^2. Afterwards we will study tranformations between these spaces which keep operation (that's why we will call them C-morphisms). At the end we will look at the "commutative" functions, i.e. maps C(H) to C(H') which can be rapresented by complex transformations C to C

**Category:** Functions and Analysis

[1] **viXra:1907.0111 [pdf]**
*submitted on 2019-07-08 06:03:23*

**Authors:** Stephen C. Pearson.

**Comments:** 48 Pages.

This particular submission contains (inter alia) copies of three (3) monographs, whose purpose is to further elaborate upon various topics having been enunciated in the author's previous set of submissions, namely - (a) "A Supplementary Discourse on the Classification and Calculus of Quaternion Hypercomplex Functions - PARTS 1/10 to 10/10."; (b) "Supplementary Notes pertaining to a Specific Quaternion Analogue of the Cauchy-Goursat Theorem.", which have been published under the 'VIXRA' Mathematics subheading:- 'Functions and Analysis'.

**Category:** Functions and Analysis