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Degenerate systems described by generalized invertible operators and controllability

Thi H. V.

Demonstratio Mathematica

2005

Vol. 38, nr 2

419--430

The theory of right invertible operators was started with works of D. Przeworska-Rolewicz and then it has been developed by M. Tasche, H. von Trotha, Z. Binderman and many other mathematicians (see [10]). Nguyen Dinh Quyet (in [5, 7]), has considered the controllability of linear system described by right invertible operators where the resolving operator is invertible. These results were generalized by A. Pogorzelec in the case of one-sized invertible resolving operator (see [9]) and by Nguyen Van Mau for the system described by generalized invertible operator (see [3]). However, for the degenerate systems, the problem has not been investigated. In this paper, we deal with the initial value problem for degenerate system of the form (2.7)-(2.8) and the controllability of this system.

On some right invertible operators in differential spaces

Multarzyński P.

Demonstratio Mathematica

2004

Vol. 37, nr 4

905--920

In this paper we consider the right invertibility problem of some linear operators defined on the algebra of smooth function on a differential space.

On the interpolation formulate induced by generalized right invertible operators

Mau N., Ngoc P.

Demonstratio Mathematica

2001

Vol. 34, nr 3

659-670