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Content available remote On the solvability of systems of linear equations on commutative semigroup
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.
This paper gives the criteria for the system of initial operators to possess the c(R)-property and the generalized c(R)-property.
Content available remote Approximate controllability for systems described by right invertible operators
In this paper, we deal with the approximate controllability for linear systems described by right invertible operators in an infinite dimensional Banach space.
This paper is to deal with the controllability of the linear system described by right invertible operators with constrained controls in Banach space.
Content available remote True shifts revisited
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.
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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