scholarly journals Splitting a linear system of operator equations with constant coefficients: A matrix polynomial approach

Filomat ◽  
2013 ◽  
Vol 27 (8) ◽  
pp. 1447-1454
Author(s):  
Nikta Shayanfar ◽  
Mahmoud Hadizadeh
Keyword(s):  
Linear System ◽  
Matrix Polynomial ◽  
Operator Equations ◽  
Constant Coefficients ◽  
System Of Operator Equations

scholarly journals Differential transcendence of solutions of systems of linear differential equations based on total reduction of the system

2020 ◽  
pp. 24-24
Author(s):  
Ivana Jovovic
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Complex Field ◽  
System Matrix ◽  
Operator Equations ◽  
Total Reduction ◽  
Commuting Operators ◽  
Constant Coefficients ◽  
Linear Differential ◽  
System Of Operator Equations

In this paper we consider total reduction of the nonhomogeneous linear system of operator equations with constant coefficients and commuting operators. The totally reduced system obtained in this manner is completely decoupled. All equations of the system differ only in the variables and in the nonhomogeneous terms. The homogeneous parts are obtained using the generalized characteristic polynomial of the system matrix. We also indicate how this technique may be used to examine differential transcendence of the solution of the linear system of the differential equations with constant coefficients over the complex field and meromorphic free terms.

scholarly journals Differential Transcendency in the Theory of Linear Differential Systems with Constant Coefficients

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
Branko Malešević ◽  
Dragana Todorić ◽  
Ivana Jovović ◽  
Sonja Telebaković
Keyword(s):  
Cauchy Problem ◽  
Linear System ◽  
Order Operator ◽  
Operator Equations ◽  
Differential Systems ◽  
First Order ◽  
Linear Differential Systems ◽  
Constant Coefficients ◽  
Linear Differential

We consider a reduction of a nonhomogeneous linear system of first-order operator equations to a totally reduced system. Obtained results are applied to Cauchy problem for linear differential systems with constant coefficients and to the question of differential transcendency.

scholarly journals Total reduction of linear systems of operator equations with the system matrix in the companion form

2013 ◽  
Vol 93 (107) ◽  
pp. 117-126
Author(s):  
Ivana Jovovic
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Characteristic Matrix ◽  
System Matrix ◽  
Operator Equations ◽  
Total Reduction ◽  
System Of Operator Equations ◽  
Separated Variables

We consider a total reduction of a nonhomogeneous linear system of operator equations with the system matrix in the companion form. Totally reduced system obtained in this manner is completely decoupled, i.e., it is a system with separated variables. We introduce a method for the total reduction, not by a change of basis, but by finding the adjugate matrix of the characteristic matrix of the system matrix. We also indicate how this technique may be used to connect differential transcendence of the solution with the coefficients of the system.

scholarly journals A saddle point type solution for a system of operator equations

2021 ◽  
pp. 1-12
Author(s):  
Piotr Kowalski
Keyword(s):  
Saddle Point ◽  
Minimax Theorem ◽  
Dirichlet Problems ◽  
Type Solution ◽  
Operator Equations ◽  
Potential Operators ◽  
System Of Operator Equations ◽  
Ky Fan ◽  
Point Type

Let Ω⊂Rn n>1 and let p,q≥2. We consider the system of nonlinear Dirichlet problems equation* brace(Au)(x)=Nu′(x,u(x),v(x)),x∈Ω,r-(Bv)(x)=Nv′(x,u(x),v(x)),x∈Ω,ru(x)=0,x∈∂Ω,rv(x)=0,x∈∂Ω,endequation* where N:R×R→R is C1 and is partially convex-concave and A:W01,p(Ω)→(W01,p(Ω))* B:W01,p(Ω)→(W01,p(Ω))* are monotone and potential operators. The solvability of this system is reached via the Ky–Fan minimax theorem.

scholarly journals Linearization of Two Second-Order Ordinary Differential Equations via Fiber Preserving Point Transformations

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Sakka Sookmee ◽  
Sergey V. Meleshko
Keyword(s):  
Linear System ◽  
General Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Point Transformations ◽  
Constant Coefficients ◽  
Linearizable System

The necessary form of a linearizable system of two second-order ordinary differential equations y1″=f1(x,y1,y2,y1′,y2′), y2″=f2(x,y1,y2,y1′,y2′) is obtained. Some other necessary conditions were also found. The main problem studied in the paper is to obtain criteria for a system to be equivalent to a linear system with constant coefficients under fiber preserving transformations. A linear system with constant coefficients is chosen because of its simplicity in finding the general solution. Examples demonstrating the procedure of using the linearization theorems are presented.

To the definition of operators , which are performed IN Kaluzhnin’s graph-schems with parafractal characteristics

2020 ◽  
pp. 98-104
Author(s):  
V.M. Simonov
Keyword(s):  
Standard Procedure ◽  
Principal Result ◽  
Operator Equations ◽  
Definition Of ◽  
System Of Operator Equations

The regular formula of operator, which is performed in given Kaluzhnin’s graph-scheme with parafractal characteristics, can be definded by two procedures. The standard procedure is based on the solution of system of operator equations, which is given birth by this graph-scheme. The modified procedure is based on the solution of several lesser-scale systems of operator equations, which are given birth by parafractals. The modified procedure is simpler than the standard one, but it is not evident identity of the results of both procedures. The principal result of this article is the theorem about this identity.

Multivariate version of slant Toeplitz operators on the Lebesgue space

2021 ◽  
pp. 2150152
Author(s):  
Shesh Kumar Pandey ◽  
Gopal Datt
Keyword(s):  
Toeplitz Operator ◽  
Lebesgue Space ◽  
Spectral Properties ◽  
Toeplitz Operators ◽  
Operator Equations ◽  
System Of Operator Equations

The paper introduces the [Formula: see text]th-order slant Toeplitz operator on the Lebesgue space of [Formula: see text]-torus, where [Formula: see text] such that [Formula: see text] for all [Formula: see text]. It investigates certain properties of [Formula: see text]th-order slant Toeplitz operators on the Lebesgue space [Formula: see text]. The paper deals with a system of operator equations, characterizing the [Formula: see text]th-order slant Toeplitz operators. At the end, we discuss certain spectral properties of the considered operator.

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