On Invertibility of Some Functional Operators with Shift  

作　　者：Aleksandr Karelin Anna Tarasenko Manuel Gonzalez-Hernandez Aleksandr Karelin;Anna Tarasenko;Manuel Gonzalez-Hernandez(Institute of Basic Sciences and Engineering, Hidalgo State University, Pachuca, Mexico)

机构地区：[1]Institute of Basic Sciences and Engineering, Hidalgo State University, Pachuca, Mexico

出　　处：《Applied Mathematics》2022年第8期651-657,共7页应用数学（英文）

摘　　要：In this paper, we consider operators arising in the modeling of renewable systems with elements that can be in different states. These operators are functional operators with non-Carlemann shifts and they act in Holder spaces with weight. The main attention was paid to non-linear equations relating coefficients to operators with a shift. The solutions of these equations were used to reduce the operators under consideration to operators with shift, the invertibility conditions for which were found in previous articles of the authors. To construct the solution of the non-linear equation, we consider the coefficient factorization problem (the homogeneous equation with a zero right-hand side) and the jump problem (the non-homogeneous equation with a unit coefficient). The solution of the general equation is represented as a composition of the solutions to these two problems.In this paper, we consider operators arising in the modeling of renewable systems with elements that can be in different states. These operators are functional operators with non-Carlemann shifts and they act in Holder spaces with weight. The main attention was paid to non-linear equations relating coefficients to operators with a shift. The solutions of these equations were used to reduce the operators under consideration to operators with shift, the invertibility conditions for which were found in previous articles of the authors. To construct the solution of the non-linear equation, we consider the coefficient factorization problem (the homogeneous equation with a zero right-hand side) and the jump problem (the non-homogeneous equation with a unit coefficient). The solution of the general equation is represented as a composition of the solutions to these two problems.

关 键 词：Operator with a Non-Carlemann Shift Inverse Operator Non-Linear Equation Factorization of Coefficient Equation with Unit Coefficient 

分 类 号：O177[理学—数学]