Howmuch information does the sequence of integer moments carry about the corresponding unknown absolutely continuous distribution? We prove that a reliable evaluation of the corresponding Shannon entropy can be done by exploiting some known theoretical results on the entropy convergence, uniquely involving exact moments without solving the underlying moment problem. All the procedure essentiall...

Linear systems of neutral type are considered using the infinite dimensional approach. The main problems are asymptotic, non-exponential stability, exact controllability and regular asymptotic stabilizability. The main tools are the moment problem approach, the Riesz basis of invariant subspaces and the Riesz basis of family of exponentials.

Set-membership estimation is in general referred in literature as the deterministic approach to state estimation, since its solution can be formulated in the context of set-valued calculus and no stochastic calculations are necessary. This turns out not to be entirely true. In this paper, we show that set-membership estimation can be equivalently formulated in the stochastic setting by employin...

Estimation theory has been developed over centuries. There are several approaches to utilizing this theory; in this chapter, these approaches are classified into three types. Type I includes the oldest two methods, the least squares (LS) and moment methods; both of these methods are non-optimal estimators. The least squares method was introduced by Carl Friedrich Gauss. Least squares problems f...

by using the trigonometric uniform splines of order 3 with a real tension factor, a numericalmethod is developed for solving a linear second order boundary value problems (2vbp) withdirichlet, neumann and cauchy types boundary conditions. the moment at the knots isapproximated by central finite-difference method. the order of convergence of the methodand the theory is illustrated by solving tes...

The exact controllability to the origin for linear evolution control equation is considered.The problem is investigated by its transformation to infinite linear moment problem. Conditions for the existence of solution for infinite linear moment problem has been obtained. The obtained results are applied to the zero controllability for control evolution equations.