scholarly journals Linear operators on Köthe spaces of vector fields

2013 ◽  
Vol 21 (2) ◽  
pp. 53-80
Author(s):  
Ion Chiţescu ◽  
Liliana Sireţchi
Keyword(s):  
Integral Representation ◽  
Representation Theorem ◽  
Vector Fields ◽  
Linear Operators ◽  
Köthe Spaces

Abstract The study of Köthe spaces of vector fields was initiated by the present authors. In this paper linear operators on these spaces are studied. An integral representation theorem is given and special types of linear operators are introduced and studied.

scholarly journals On linear operators and bases on Köthe spaces

2016 ◽  
Vol 1 (2) ◽  
pp. 617-624 ◽  
Author(s):  
M. Maldonado ◽  
J. Prada ◽  
M. J. Senosiain
Keyword(s):  
Analytic Functions ◽  
Generalized Derivation ◽  
Weighted Shift ◽  
Linear Operators ◽  
Shift Operators ◽  
Köthe Spaces ◽  
Unilateral Weighted Shift ◽  
Spaces Of Analytic Functions

AbstractWe make a survey of results published by the authors about the backward and forward unilateral weighted shift operators in Kóthe spaces, the so-called generalized derivation and integration operators, extending well-known results for spaces of analytic functions.

MULTIPERIODIC SOLUTIONS OF SECOND-ORDER SYSTEMS WITH DIFFERENTIATION OPERATOR ON THE LYAPUNOV'S VECTOR FIELD

2020 ◽  
Vol 69 (1) ◽  
pp. 155-163
Author(s):  
B.Zh. Omarova ◽  
Keyword(s):  
Integral Representation ◽  
Vector Fields ◽  
Homogeneous System ◽  
Differentiation Operator ◽  
Second Order ◽  
Inhomogeneous System ◽  
Representation Of Solutions ◽  
Real Analytic ◽  
Time Variables ◽  
Second Order Systems

The problem of the existence and integral representation of a unique multiperiodic solution of a second-order linear inhomogeneous system with constant coefficients and a differentiation operator on the direction of the main diagonal of the space of time variables and of the vector fields in the form of Lyapunov systems with respect to space variables were considered. The multiperiodicity of zeros of this operator and the condition for the absence of a nonzero multiperiodic and real-analytic solution of the homogeneous system corresponding to the given system are established. An integral representation of solutions of an inhomogeneous linear autonomous system that multiperiodic in time variables and realanalytic in space variables is obtained. The existence theorem of a unique multiperiodic in time variables and real-analytic in space variables solutions of the original linear system in terms of the Green's function under sufficiently general conditions is substantiated.

scholarly journals Integration in Orlicz-Bochner Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Marian Nowak
Keyword(s):  
Integral Representation ◽  
Measure Space ◽  
Finite Measure ◽  
Linear Operators ◽  
Continuous Linear ◽  
Topological Properties ◽  
Young Function ◽  
Finite Measure Space ◽  
Bochner Space ◽  
Continuous Linear Operators

Let (Ω,Σ,μ) be a complete σ-finite measure space, φ be a Young function, and X and Y be Banach spaces. Let Lφ(X) denote the Orlicz-Bochner space, and Tφ∧ denote the finest Lebesgue topology on Lφ(X). We study the problem of integral representation of (Tφ∧,·Y)-continuous linear operators T:Lφ(X)→Y with respect to the representing operator-valued measures. The relationships between (Tφ∧,·Y)-continuous linear operators T:Lφ(X)→Y and the topological properties of their representing operator measures are established.

Sign in / Sign up

Export Citation Format

Share Document