Related papers: Truncated moment problems in the class of generali…
The truncated moment problem asks to characterize finite sequences of real numbers that are the moments of a positive Borel measure on Rn. Its tracial analog is obtained by integrating traces of symmetric matrices and is the main topic of…
The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment…
A moment problem is presented for a class of signed measures which are termed pseudo-positive. Our main result says that for every pseudo-positive definite functional (subject to some reasonable restrictions) there exists a representing…
In this paper we study truncated moment problems for $J$-self-adjoint, $J$-skew-self-adjoint and $J$-unitary operators. Conditions of the solvability are given. Some canonical solutions of the moment problems are constructed. As a…
In this paper we develop a new approximation method valid for a wide family of nonlinear wave equations of Nonlinear Schr\"odinger type. The result is a reduced set of ordinary differential equations for a finite set of parameters measuring…
We consider the problem of finding a (non-negative) measure $\mu$ on $\mathfrak{B}(\mathbb{C}^n)$ such that $\int_{\mathbb{C}^n} \mathbf{z}^{\mathbf{k}} d\mu(\mathbf{z}) = s_{\mathbf{k}}$, $\forall \mathbf{k}\in\mathcal{K}$. Here…
In this paper, we devote our interest to solving the real cubic truncated moment problem. We provide some results that allow to get a complete solution via a minimal representing measure. Some numerical examples are also presented to…
We present tracial analogs of the classical results of Curto and Fialkow on moment matrices. A sequence of real numbers indexed by words in non-commuting variables with values invariant under cyclic permutations of the indexes, is called a…
We classify all functions which, when applied term by term, leave invariant the sequences of moments of positive measures on the real line. Rather unexpectedly, these functions are built of absolutely monotonic components, or reflections of…
The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated…
Generalized moment problems optimize functional expectation over a class of distributions with generalized moment constraints, i.e., the function in the moment can be any measurable function. These problems have recently attracted growing…
The general entire solution to a linear system of moment differential equations is obtained in terms of a moment kernel function for generalized summability, and the Jordan decomposition of the matrix defining the problem. The growth at…
We summarize significant classical results on (in)determinacy of measures in terms of their finite positive integer order moments. Well-known is the role of the smallest eigenvalues of Hankel matrices, starting from Hamburger's results a…
We characterize the existence of the Lebesgue integrable solutions of the truncated problem of moments in several variables on unbounded supports by the existence of some maximum entropy -- type representing densities and discuss a few…
We expose in full detail a constructive procedure to invert the so--called "finite Markov moment problem". The proofs rely on the general theory of Toeplitz matrices together with the classical Newton's relations.
A complete analytic solution for the time-optimal control problem for nonlinear control systems of the form $\dot x_1=u$, $\dot x_j=x_1^{j-1}$, $j=2,\ldots,n$, is obtained for arbitrary $n$. The main goal of the paper is to present the…
We find necessary and sufficient conditions for the existence of a probability measure on $\mathbb{N}_0$, the nonnegative integers, whose first $n$ moments are a given $n$-tuple of nonnegative real numbers. The results, based on finding an…
The main result of the paper is an interesting relation between the solution of the truncated Exponential Moment problem and truncated Classical Moment problem, considered on the half-line or on a compact interval.
In this paper, we propose a new easily implementable method for solving a class of semi-infinite programs, where an approximate linear semidefinite program is constructed for the concerned semi-infinite program based on the duality theory…
The Hamburger moment problem for the $q$-Lommel polynomials which are related to the Hahn-Exton $q$-Bessel function is known to be indeterminate for a certain range of parameters. In this paper, the Nevanlinna parametrization for the…