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1
Content available remote On the solvability of systems of linear equations on commutative semigroup
Huyen N. T. T., Tuan N. M.
Demonstratio Mathematica
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2010
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Vol. 43, nr 4
865-876
EN
This paper deals with the solvability of systems of linear operator equations in a linear space. Namely, the paper provides necessary and sufficient conditions for the operators under which certain kinds of systems of operator equations are solvable.
2
Content available remote On the criteria for initial operators possessing (c)- property and generalized (c)-propertty
Mau N., Tuan N.
Demonstratio Mathematica
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2008
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Vol. 41, nr 4
805-811
EN
This paper gives the criteria for the system of initial operators to possess the c(R)-property and the generalized c(R)-property.
3
Content available remote Approximate controllability for systems described by right invertible operators
Hoang V. T.
Control and Cybernetics
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2008
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Vol. 37, no 1
39-50
EN
In this paper, we deal with the approximate controllability for linear systems described by right invertible operators in an infinite dimensional Banach space.
4
Content available remote The controllability of the system described by right invertible operators with constrained controls
Thi H.
Demonstratio Mathematica
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2006
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Vol. 39, nr 3
599-608
EN
This paper is to deal with the controllability of the linear system described by right invertible operators with constrained controls in Banach space.
5
Content available remote True shifts revisited
Przeworska-Rolewicz D.
Demonstratio Mathematica
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2001
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Vol. 34, nr 1
111-122
6
Content available An algebraic analysis approach to 2-D discrete problems
Przeworska-Rolewicz D., Wysocki H.
Control and Cybernetics
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2001
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Vol. 30, no 2
149-158
EN
A model of algebraic analysis for the 2-index sequences (of the type 2-D) is considered. For difference operators of the form D{x_m,n}:= {x_m+1,n+1 - A_m,nX_m,n} the right inverses and the corresponding initial operators are constructed. Having already known the initial operators, one can determine solutions of the corresponding initial value problems.
7
Content available remote Linear combinations of right invertible operators in commutative algebras with logarithms
Przeworska-Rolewicz D.
Demonstratio Mathematica
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1998
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Vol. 31, nr 4
887-898
EN
It is well known that a power of a right invertible operators is again right invertible, as well as a polynomial in a right invertible operator under appropriate assumptions. However , a linear combination of right invertible operators (in particular , their sum and/or difference) in general is not right invertible. It will be shown how to solve equations with linear combinations of right invertible operators in commutative algebras using properties of logarithmic and antilogarithmic mappings. The used method is, in a sense, a kind of the variables separation method. We shall obtain also an analogue of the classical Fourier method for partial differential equations. Note that results concerning the Fourier method are proved under weaker assumptions than those obtained in PR[l] (cf. also PR[2]). The extensive bibliography of the subject can be found in PR[2] and PR[4].
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