A representation theorem for quantum systems

Dosi, Anar
In this note representations of quantum systems are investigated. We propose a unital bipolar theorem for unital quantum cones, which plays a key role in proving a representation theorem for quantum systems. It turns out that each quantum system is identified with a certain quantum L-a-system up to a quantum order isomorphism.


Leblebicioğlu, Mehmet Kemal (Elsevier BV, 1992-02-01)
In this article some of the results for optimal control of linear systems have been generalized to a nonlinear case. This is achieved by employing standard techniques of the nonlinear theory. After demonstrating the existence of optimal controls, finite element method is used to discretize the problem. The resulting finite dimensional problem is solved by a special algorithm. The theoretical discussions are completed by proving that approximate solutions are reduced to exact solutions as the element size te...
On the smoothness of solutions of impulsive autonomous systems
Akhmet, Marat (Elsevier BV, 2005-01-01)
The aim of this paper is to investigate dependence of solutions on parameters for nonlinear autonomous impulsive differential equations. We will specify what continuous, differentiable and analytic dependence of solutions on parameters is, define higher order derivatives of solutions with respect to parameters and determine conditions for existence of such derivatives. The theorem of analytic dependence of solutions on parameters is proved.
Nonautonomous Bifurcations in Nonlinear Impulsive Systems
Akhmet, Marat (Springer Science and Business Media LLC, 2020-01-01)
In this paper, we study existence of the bounded solutions and asymptotic behavior of an impulsive Bernoulli equations. Nonautonomous pitchfork and transcritical bifurcation scenarios are investigated. An examples with numerical simulations are given to illustrate our results.
Generalization of a theorem of Bohr for bases in spaces of holomorphic functions of several complex variables
Aizenberg, L; Aytuna, A; Djakov, P (Elsevier BV, 2001-06-15)
In the first part, we generalize the classical result of Bohr by proving that an analogous phenomenon occurs whenever D is an open domain in C-m (or, more generally, a complex manifold) and (phi (n))(n=0)(infinity) is a basis in the space of holomorphic functions H(D) such that phi (0) = 1 and phi (n)(z(0)) = 0, n greater than or equal to 1, for some z(0) is an element of D. Namely, then there exists a neighborhood U of the point to such that, whenever a holomorphic function on D has modulus less than 1, th...
Dosi, Anar (American Mathematical Society (AMS), 2011-02-01)
In the present paper we introduce quantum measures as a concept of quantum functional analysis and develop the fractional space technique in the quantum (or local operator) space framework. We prove that each local operator algebra (or quantum *-algebra) has a fractional space realization. This approach allows us to formulate and prove a noncommutative Albrecht-Vasilescu extension theorem, which in turn solves the quantum moment problem.
Citation Formats
A. Dosi, “A representation theorem for quantum systems,” FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, pp. 241–245, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63629.