An approach to the dynamical inverse problems (IP's) based upon their relations to the Boundary Control Theory (the so-called BC-method) is developed. The method is applied to the problem of reconstruction of a vector eld given on a Riemannian manifold via the response operator (the dynamical Dirichlet-to-Neumann map). A peculiarity of the case under consideration is that the operator which gov...

1 Basic definitions In this paper, we present a description of a collaboration with K. Guo, W. Lim, A. Savov and E. Wilson. We make use of the Fourier transform f → ˆ f that, for f ∈ L 1 (R n), is defined asˆf (ξ) = R n f (x) e −2πiξx dx. As is well-known, this operator has a unique extension to L 2 (R n) that is a unitary operator. In the following, we refer to the domain ofˆf as the " frequen...

We characterize by boundary conditions the Krein-von Neumann extension of a strictly positive minimal operator corresponding to regular even order quasi-differential expression Shin-Zettl type. The characterization is stated in terms specially chosen basis for kernel maximal and employs description Friedrichs due Möller Zettl.

In this paper, we state some results on product of operators with closed ranges and we solve the operator equation $TXS^*-SX^*T^*= A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $TS = 1$. Furthermore, by using some block operator matrix techniques, we nd explicit solution of the operator equation $TXS^*-SX^*T^*= A$.

In this work we summarize our recent results on extending Description Logics for reasoning about prototypical properties and inheritance with exceptions. First, we focus our attention on the logic ALC. We present a nonmonotonic logic ALC + Tmin, which is built upon a monotonic logic ALC+T obtained by adding a typicality operator T to ALC. The operator T is intended to select the “most normal” o...

We propose a new operator interpretation for the lattice paths of the unitary minimal models M(k + 1, k + 2). These operators are akin to the modes of a complex fermion, but at the same time, they capture some characteristics of Z k parafermions in that there is a bound on the number of allowed successive operators (which is k − 1). The operators act non-locally on the path: Their action modifi...

‎in this paper we try to extend geometric concepts in the context of operator valued tensors‎. ‎to this end‎, ‎we aim to replace the field of scalars $ mathbb{r} $ by self-adjoint elements of a commutative $ c^star $-algebra‎, ‎and reach an appropriate generalization of geometrical concepts on manifolds‎. ‎first‎, ‎we put forward the concept of operator-valued tensors and extend semi-riemannian...

We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it a pure state of some quantum system is described by a state section (along paths) of a (Hilbert) fibre bund...

The present paper focuses on the dynamical systems of quadratic bistochastic operators (QBO) standard simplex. In paper, we show character connection a operator with extreme operators. addition, prove that almost all are strictly regular and give description in convex polytope QBO. Furthermore, density set QBO is proved nontrivial examples given.

The theory of abstract Friedrichs operators, introduced by Ern, Guermond and Caplain (2007), proved to be a successful setting for studying positive symmetric systems first order partial differential equations (Friedrichs, 1958), nowadays better known as systems. Recently, Antoni\'c, Michelangeli Erceg (2017) presented purely operator-theoretic description allowing application the universal ope...