Open AccessDecomposition of abstract linear operators in Banach spaces
Author(s) -
Kyriaki Tsilika
Publication year - 2021
Publication title -
informacionno-upravlâûŝie sistemy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.202
H-Index - 6
eISSN - 2541-8610
pISSN - 1684-8853
DOI - 10.31799/1684-8853-2021-2-2-12
Subject(s) - mathematics , banach space , finite rank operator , uniqueness , operator (biology) , correctness , c0 semigroup , unbounded operator , operator theory , algebra over a field , decomposition , pure mathematics , linear map , approximation property , mathematical analysis , algorithm , biochemistry , chemistry , repressor , transcription factor , gene , ecology , biology
In this paper we investigate a class of integro-differential equations οn a Banach space with nonlocal and initial boundary conditions in terms of an abstract operator equation
B1 x=Ax-S0 F(A x)-G0 Φ(Ax)=f ,x∈D(B1) (1)
where A, A are linear abstract operators, S0, G0 are vectors and Φ, F the functional vectors. The operator B1 under study has a decomposition of the form B1=B0 B with B and B0 being different abstract linear operators of special forms. Methods. Extensions of operators on Banach spaces are used. The Decomposition Method proposed here is essentially different from other Decomposition Methods in the relevant literature. Results. Our main research result is the existence and uniqueness of solution of and its representation in the closed form. The necessary and sufficient conditions for the correctness of the operator are intermediate, secondary results. Overall, a direct method analytically solving problem (1) is proposed, in an algorithmic procedure that is reproducible in any program of symbolic calculations. The stages of the solution method are illustrated by three examples. Computer algebra system Mathematica is employed to demonstrate the solution outcomes.