Corpus ID: 119707908

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
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 theExpand
Quadratic Equation over Associative D-Algebra
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 theExpand
Differential Equations and the Calculus of Variations
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
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 theExpand
Floquet Theory for Quaternion-Valued Differential Equations
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 andExpand
Lectures on Linear Algebra over Division Ring
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
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 quaternionExpand
Linear Map of $D$-Algebra
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
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-rowExpand
Introduction into Calculus over Division Ring
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. IExpand
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