# Functions and Analysis

## 1910 Submissions

 viXra:1910.0518 [pdf] replaced on 2019-10-31 05:38:42

### Elementary Aspects of the Fundamental Theorem of Algebra

Authors: Timothy W. Jones

We motivate and give a proof of the fundamental theorem of algebra using high school algebra.
Category: Functions and Analysis

 viXra:1910.0414 [pdf] submitted on 2019-10-21 19:54:08

### Divergence Series and Integrals From the Viewpoint of the Division by Zero Calculus

Authors: Saburou Saitoh
Comments: 8 Pages. In this short note, we would like to refer to the fundamental new interpretations that for the fundamental expansion $1/(1-z) = \sum_{j=0}^{\infty} z^j$ it is valid in the sense $0=0$ for $z=1$, for the integral $\int_1^{\infty} 1/x dx$ it is zero and i

In this short note, we would like to refer to the fundamental new interpretations that for the fundamental expansion $1/(1-z) = \sum_{j=0}^{\infty} z^j$ it is valid in the sense $0=0$ for $z=1$, for the integral $\int_1^{\infty} 1/x dx$ it is zero and in the formula $\int_0^{\infty} J_0(\lambda t) dt = 1/\lambda$, it is valid with $0=0$ for $\lambda =0$ in the sense of the division by zero.
Category: Functions and Analysis

 viXra:1910.0245 [pdf] submitted on 2019-10-15 11:22:08

### Complex Hadamard Matrices and Applications

Authors: Teo Banica
A complex Hadamard matrix is a square matrix $H\in M_N(\mathbb C)$ whose entries are on the unit circle, $|H_{ij}|=1$, and whose rows and pairwise orthogonal. The main example is the Fourier matrix, $F_N=(w^{ij})$ with $w=e^{2\pi i/N}$. We discuss here the basic theory of such matrices, with emphasis on geometric and analytic aspects.