# Differential Equation over Banach Algebra

@inproceedings{Kleyn2018DifferentialEO, title={Differential Equation over Banach Algebra}, author={A. Kleyn}, year={2018} }

In the book, I considered differential equations of order $1$ over Banach $D$-algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. In noncommutative Banach algebra, initial value problem for linear homogeneous equation has infinitely many solutions.

#### References

SHOWING 1-10 OF 18 REFERENCES

Linear Mappings of Quaternion Algebra

- Mathematics
- 2011

In the paper I considered linear and antilinear automorphisms of quaternion algebra. I proved the theorem that there is unique expansion of R-linear mapping of quaternion algebra relative to the… Expand

Quadratic Equation over Associative D-Algebra

- Mathematics
- 2018

In this paper, I treat quadratic equation over associative $D$-algebra. In quaternion algebra $H$, the equation $x^2=a$ has either $2$ roots, or infinitely many roots. Since $a\in R$, $a<0$, then the… Expand

Differential Equations and the Calculus of Variations

- Mathematics
- 2003

Differential equations and the calculus of variations , Differential equations and the calculus of variations , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

Linear Mappings of Free Algebra

- Mathematics, Physics
- 2010

For arbitrary universal algebra, in which the operation of addition is defined, I explore biring of matrices of mappings. The sum of matrices is determined by the sum in universal algebra, and the… Expand

Floquet Theory for Quaternion-Valued Differential Equations

- Mathematics
- 2019

This paper describes the Floquet theory for quaternion-valued differential equations (QDEs). The Floquet normal form of fundamental matrix for linear QDEs with periodic coefficients is presented and… Expand

Lectures on Linear Algebra over Division Ring

- Mathematics
- 2007

In this book i treat linear algebra over division ring. A system of linear equations over a division ring has properties similar to properties of a system of linear equations over a field. However,… Expand

Correspondence between Row-Column Determinants and Quasideterminants of Matrices over Quaternion Algebra

- Mathematics
- 2011

In this paper, we considered the theory of quasideterminants and row and column determinants. We considered the application of this theory to the solving of a system of linear equations in quaternion… Expand

Linear Map of $D$-Algebra

- Mathematics
- 2015

Module is effective representation of ring in Abelian group. Linear map of module over commutative ring is morphism of corresponding representation. This definition is the main subject of the book. … Expand

Linear differential systems over the quaternion skew field

- Mathematics
- 2018

A basic theory on the first order right and left linear quaternion differential systems (LQDS) is given systematic in this paper. To proceed the theory of LQDS we adopt the theory of column-row… Expand

Introduction into Calculus over Division Ring

- Mathematics
- 2010

Based on twin representations of division ring in an Abelian group I consider $D$\Hyph vector spaces over division ring. Morphism of $D$\Hyph vector spaces is linear map of $D$\Hyph vector spaces.
I… Expand