Related papers: On the truncated matrix power moment problem with …
In the field of orthogonal polynomials theory, the classical Markov theorem shows that for determinate moment problems the spectral measure is under control of the polynomials asymptotics. The situation is completely different for…
The time-dependent Schrodinger equation is solved for two model problems for a non-Hermitian quantum system.A simple matrix model system is used to examine two critical problems for these systems: complex and non-observable energies and…
Let ${\cal X }=XX^{\prime}$ be a random matrix associated with a centered $r$-column centered Gaussian vector $X$ with a covariance matrix $P$. In this article we compute expectations of matrix-products of the form $\prod_{1\leq i\leq…
In a 2014 paper, R.E. Curto and S. Yoo proved that a moment matrix $M(3)$ with specific harmonic polynomials as column relations admits a representing measure if and only if a condition at the level of moments holds. \ In this paper, we…
The method of truncated Mellin moments in a solving QCD evolution equations of the nonsinglet structure functions $F_2^{NS}(x,Q^2)$ and $g_1^{NS}(x,Q^2)$ is presented. All calculations are performed within double logarithmic $ln^2x$…
Many real life problems can be reduced to the solution of a complex exponentials approximation problem which is usually ill posed. Recently a new transform for solving this problem, formulated as a specific moments problem in the plane, has…
The model reduction problem for high-order multi-input, multi-output (MIMO) polynomial nonlinear systems based on moment matching is addressed. The technique of power-series decomposition is exploited: this decomposes the solution of the…
Because of the finiteness of the life span and boundedness of the physical space, the more reasonable or physical choice is the tempered power-law instead of pure power-law for the CTRW model in characterizing the waiting time and jump…
We present the new Guided Moments ($\texttt{GM}$) formalism for neutrino modeling in astrophysical scenarios like core-collapse supernovae and neutron star mergers. The truncated moments approximation ($\texttt{M1}$) and Monte-Carlo…
We derive the LO DGLAP evolution equation for the full Mellin moments of the truncated at $x_0$ first moment of the nonsinglet parton distribution. This "moment of moment" approach allows to determine the small-$x_0$ behaviour of the…
The conditional moment problem is a powerful formulation for describing structural causal parameters in terms of observables, a prominent example being instrumental variable regression. A standard approach reduces the problem to a finite…
This paper considers the sparse eigenvalue problem, which is to extract dominant (largest) sparse eigenvectors with at most $k$ non-zero components. We propose a simple yet effective solution called truncated power method that can…
These are ten lectures on the moment problem delivered by the author at the Vietnam Institute of Advanced Studies in Mathematics, Hanoi, March 2019. The first 3 lectures are about the one-dimensional full and truncated moment problem. The…
Let $\beta\equiv\beta^{(2n)}$ be an N-dimensional real multi-sequence of degree 2n, with associated moment matrix $\mathcal{M}(n)\equiv \mathcal{M}(n)(\beta)$, and let $r:=rank \mathcal{M}(n)$. We prove that if $\mathcal{M}(n)$ is positive…
The main goal of the paper is to parametrize the Weyl matrix balls associated with an arbitrary matricial truncated Hamburger moment problem. For the special case of a non-degenerate matricial truncated Hamburger moment problem the…
Let Q(x,y)=0 be an hyperbola in the plane. Given real numbers $\beta \equiv\beta^{2n)}=\{\beta_{ij}\}_{i,j\geq0,i+j\leq2n}$, with $\beta_{00}>0$, the truncated Q-hyperbolic moment problem for \beta entails finding necessary and sufficient…
Moment methods are classical approaches that approximate the mesoscopic radiative transfer equation by a system of macroscopic moment equations. An expansion in the angular variables transforms the original equation into a system of…
We assume that a finite set of moments of a random vector is given. Its underlying density is unknown. An algorithm is proposed for efficiently calculating Dirac mixture densities maintaining these moments while providing a homogeneous…
The Nevanlinna parametrization establishes a bijection between the class of all measures having a prescribed set of moments and the class of Pick functions. The fact that all measures constructed through the Nevanlinna parametrization have…
In experiment, the multiplicity distributions of inelastic processes are truncated due to finite energy, insufficient statistics or special choice of events. It is shown that the moments of such truncated multiplicity distributions possess…